@article{holliday_lindner_ditto_2023, title={Solving quantum billiard eigenvalue problems with physics-informed machine learning}, volume={13}, ISSN={["2158-3226"]}, DOI={10.1063/5.0161067}, abstractNote={A particle confined to an impassable box is a paradigmatic and exactly solvable one-dimensional quantum system modeled by an infinite square well potential. Here, we explore some of its infinitely many generalizations to two dimensions, including particles confined to rectangle-, ellipse-, triangle-, and cardioid-shaped boxes using physics-informed neural networks. In particular, we generalize an unsupervised learning algorithm to find the particles’ eigenvalues and eigenfunctions, even in cases where the eigenvalues are degenerate. During training, the neural network adjusts its weights and biases, one of which is the energy eigenvalue, so that its output approximately solves the stationary Schrödinger equation with normalized and mutually orthogonal eigenfunctions. The same procedure solves the Helmholtz equation for the harmonics and vibration modes of waves on drumheads or transverse magnetic modes of electromagnetic cavities. Related applications include quantum billiards, quantum chaos, and Laplacian spectra.}, number={8}, journal={AIP ADVANCES}, author={Holliday, Elliott G. G. and Lindner, John F. F. and Ditto, William L. L.}, year={2023}, month={Aug} }
 @article{murali_ditto_sinha_2022, title={Reconfigurable Noise-Assisted Logic Gates Exploiting Nonlinear Transformation of Input Signals}, volume={18}, ISSN={["2331-7019"]}, url={https://doi.org/10.1103/PhysRevApplied.18.014061}, DOI={10.1103/PhysRevApplied.18.014061}, abstractNote={We demonstrate the direct implementation of all basic logical operations utilizing a single bistable system driven by nonlinearly transformed input signals, in the presence of noise. Exploiting the hopping between the dynamical states of the bistable system, assisted by the noise floor, in response to the transformed inputs, allows the implementation of the full set of logic operations. So this idea can form the basis of the design of a dynamical computing element that can be rapidly morphed to yield any desired logic gate by varying just a single control parameter. Further, the results are verified in electronic circuit experiments, demonstrating the robustness of the concept and the potential of this idea to be realized in wide-ranging systems.}, number={1}, journal={PHYSICAL REVIEW APPLIED}, author={Murali, K. and Ditto, W. L. and Sinha, Sudeshna}, year={2022}, month={Jul} }
 @article{murali_rajasekar_aravind_kohar_ditto_sinha_2021, title={Construction of logic gates exploiting resonance phenomena in nonlinear systems}, volume={379}, ISSN={["1471-2962"]}, DOI={10.1098/rsta.2020.0238}, abstractNote={A two-state system driven by two inputs has been found to consistently produce a response mirroring a logic function of the two inputs, in an optimal window of moderate noise. This phenomenon is called logical stochastic resonance (LSR). We extend the conventional LSR paradigm to implement higher-level logic architecture or typical digital electronic structures via carefully crafted coupling schemes. Further, we examine the intriguing possibility of obtaining reliable logic outputs from a noise-free bistable system, subject only to periodic forcing, and show that this system also yields a phenomenon analogous to LSR, termed Logical Vibrational Resonance (LVR), in an appropriate window of frequency and amplitude of the periodic forcing. Lastly, this approach is extended to realize morphable logic gates through the Logical Coherence Resonance (LCR) in excitable systems under the influence of noise. The results are verified with suitable circuit experiments, demonstrating the robustness of the LSR, LVR and LCR phenomena. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.}, number={2192}, journal={PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES}, author={Murali, K. and Rajasekar, S. and Aravind, Manaoj V. and Kohar, Vivek and Ditto, W. L. and Sinha, Sudeshna}, year={2021}, month={Mar} }
 @article{choudhary_lindner_holliday_miller_sinha_ditto_2021, title={Forecasting Hamiltonian dynamics without canonical coordinates}, volume={103}, ISSN={["1573-269X"]}, DOI={10.1007/s11071-020-06185-2}, abstractNote={Conventional neural networks are universal function approximators, but they may need impractically many training data to approximate nonlinear dynamics. Recently introduced Hamiltonian neural networks can efficiently learn and forecast dynamical systems that conserve energy, but they require special inputs called canonical coordinates, which may be hard to infer from data. Here, we prepend a conventional neural network to a Hamiltonian neural network and show that the combination accurately forecasts Hamiltonian dynamics from generalised noncanonical coordinates. Examples include a predator–prey competition model where the canonical coordinates are nonlinear functions of the predator and prey populations, an elastic pendulum characterised by nontrivial coupling of radial and angular motion, a double pendulum each of whose canonical momenta are intricate nonlinear combinations of angular positions and velocities, and real-world video of a compound pendulum clock.}, number={2}, journal={NONLINEAR DYNAMICS}, author={Choudhary, Anshul and Lindner, John F. and Holliday, Elliott G. and Miller, Scott T. and Sinha, Sudeshna and Ditto, William L.}, year={2021}, month={Jan}, pages={1553–1562} }
 @article{murali_sinha_kohar_ditto_2021, title={Harnessing tipping points for logic operations}, volume={230}, ISSN={["1951-6401"]}, DOI={10.1140/epjs/s11734-021-00014-2}, number={16-17}, journal={EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS}, author={Murali, K. and Sinha, Sudeshna and Kohar, Vivek and Ditto, William L.}, year={2021}, month={Oct}, pages={3403–3409} }
 @article{miller_lindner_choudhary_sinha_ditto_2021, title={Negotiating the separatrix with machine learning}, volume={12}, ISSN={["2185-4106"]}, url={https://doi.org/10.1587/nolta.12.134}, DOI={10.1587/nolta.12.134}, number={2}, journal={IEICE NONLINEAR THEORY AND ITS APPLICATIONS}, author={Miller, Scott T. and Lindner, John F. and Choudhary, Anshul and Sinha, Sudeshna and Ditto, William L.}, year={2021}, pages={134–142} }
 @article{boccaletti_mindlin_ditto_atangana_2020, title={Closing editorial: Forecasting of epidemic spreading: lessons learned from the current covid-19 pandemic}, volume={139}, ISSN={["1873-2887"]}, DOI={10.1016/j.chaos.2020.110278}, abstractNote={The entire world is currently fighting the severe and dangerous pandemic COVID-19, which is causing bodily suffering and mental distress due to the rapidly increasing number of infected patients and deaths worldwide. Many COVID-19 treatments are going on in India, and some treatments are under development for these patients. But, treatment selection for the COVID-19 patients is challenging in the present situation. Through the multi-criteria decision-making technique, they can select the COVID-19 treatments easily. Therefore, we have developed an MCDM technique to select COVID-19 treatments in India. This paper invented the value and ambiguity of bipolar fuzzy (BF) numbers. Additionally, some fundamental theorems and properties of BF-numbers are studied. A novel positive and negative interpreter ranking index of BF numbers has been introduced. In the present day, most human decision-making relies heavily on bipolar fuzzy information. Hence, we developed an MCDM technique with bipolar fuzzy details. A comprehensive range of human decisions for selecting COVID-19 treatments is based on positive and negative double-sided or bipolar judgemental thinking. To select COVID-19 treatments in India, we have applied the proposed MCDM technique with BTrF information. Moreover, to demonstrate the applicability of our proposed MCDM method, we have considered a numerical example with BF data. Finally, we give the comparison study to show the effectiveness of our proposed MCDM method with other existing decision-making methods.}, journal={CHAOS SOLITONS & FRACTALS}, author={Boccaletti, Stefano and Mindlin, Gabriel and Ditto, William and Atangana, Abdon}, year={2020}, month={Oct} }
 @article{kia_mendes_parnami_george_mobley_ditto_2020, title={Nonlinear dynamics based machine learning: Utilizing dynamics-based flexibility of nonlinear circuits to implement different functions}, volume={15}, url={https://doi.org/10.1371/journal.pone.0228534}, DOI={10.1371/journal.pone.0228534}, abstractNote={The core element of machine learning is a flexible, universal function approximator that can be trained and fit into the data. One of the main challenges in modern machine learning is to understand the role of nonlinearity and complexity in these universal function approximators. In this research, we focus on nonlinear complex systems, and show their capability in representation and learning of different functions. Complex nonlinear dynamics and chaos naturally yield an almost infinite diversity of dynamical behaviors and functions. Physical, biological and engineered systems can utilize this diversity to implement adaptive, robust behaviors and operations. A nonlinear dynamical system can be considered as an embodiment of a collection of different possible behaviors or functions, from which different behaviors or functions can be chosen as a response to different conditions or problems. This process of selection can be manual in the sense that one can manually pick and choose the right function through directly setting parameters. Alternatively, we can automate the process and allow the system itself learn how to do it. This creates an approach to machine learning, wherein the nonlinear dynamics represents and embodies different possible functions, and it learns through training how to pick the right function from this function space. We report on how we utilized nonlinear dynamics and chaos to design and fabricate nonlinear dynamics based, morphable hardware in silicon as a physical embodiment for different possible functions. We demonstrate how this flexible, morphable hardware learns through learning and searching algorithms such as genetic algorithm to implement different desired functions. In this approach, we combine two powerful natural and biological phenomenon, Darwinian evolution and nonlinear dynamics and chaos, as a dynamics-oriented approach to designing intelligent, adaptive systems with applications. Nonlinear dynamics embodies different functions at the hardware level, while an evolutionary method is utilized in order to find the parameters to implement the right function.}, number={3}, journal={PLoS ONE}, author={Kia, B. and Mendes, A. and Parnami, A. and George, R. and Mobley, K. and Ditto, W.}, editor={Adamatzky, AndrewEditor}, year={2020}, pages={e0228534} }
 @article{choudhary_lindner_holliday_miller_sinha_ditto_2020, title={Physics-enhanced neural networks learn order and chaos}, volume={101}, url={https://doi.org/10.1103/PhysRevE.101.062207}, DOI={10.1103/PhysRevE.101.062207}, abstractNote={Conventional artificial neural networks are powerful tools in science and industry, but they can fail when applied to nonlinear systems where order and chaos coexist. We use neural networks that incorporate the structures and symmetries of Hamiltonian dynamics to predict phase space trajectories even as nonlinear systems transition from order to chaos. We demonstrate Hamiltonian neural networks on the canonical Henon-Heiles system, which models diverse dynamics from astrophysics to chemistry. The power of the technique and the ubiquity of chaos suggest widespread utility.}, number={6}, journal={Physical Review E}, author={Choudhary, A. and Lindner, J.F. and Holliday, E. and Miller, S.T. and Sinha, S. and Ditto, W.L.}, year={2020}, month={Jun}, pages={062207} }
 @article{murali_sinha_kohar_kia_ditto_2018, title={Chaotic attractor hopping yields logic operations}, volume={13}, ISSN={["1932-6203"]}, url={https://doi.org/10.1371/journal.pone.0209037}, DOI={10.1371/journal.pone.0209037}, abstractNote={Certain nonlinear systems can switch between dynamical attractors occupying different regions of phase space, under variation of parameters or initial states. In this work we exploit this feature to obtain reliable logic operations. With logic output 0/1 mapped to dynamical attractors bounded in distinct regions of phase space, and logic inputs encoded by a very small bias parameter, we explicitly demonstrate that the system hops consistently in response to an external input stream, operating effectively as a reliable logic gate. This system offers the advantage that very low-amplitude inputs yield highly amplified outputs. Additionally, different dynamical variables in the system yield complementary logic operations in parallel. Further, we show that in certain parameter regions noise aids the reliability of logic operations, and is actually necessary for obtaining consistent outputs. This leads us to a generalization of the concept of Logical Stochastic Resonance to attractors more complex than fixed point states, such as periodic or chaotic attractors. Lastly, the results are verified in electronic circuit experiments, demonstrating the robustness of the phenomena. So we have combined the research directions of Chaos Computing and Logical Stochastic Resonance here, and this approach has potential to be realized in wide-ranging systems.}, number={12}, journal={PLOS ONE}, author={Murali, K. and Sinha, Sudeshna and Kohar, Vivek and Kia, Behnam and Ditto, William L.}, editor={Adamatzky, AndrewEditor}, year={2018}, month={Dec} }
 @article{kia_mobley_ditto_2017, title={An Integrated Circuit Design for a Dynamics-Based Reconfigurable Logic Block}, volume={64}, ISSN={["1558-3791"]}, DOI={10.1109/tcsii.2016.2611442}, abstractNote={In this brief, a nonlinear integrated circuit to harvest different types of digital computation from complex dynamics is designed and fabricated. This circuit can be dynamically reconfigured to implement different two-input, one-output digital functions. The main advantage of the circuit is the ability to implement different digital functions in each clock cycle without halting for reconfiguration.}, number={6}, journal={IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS}, author={Kia, Behnam and Mobley, Kenneth and Ditto, William L.}, year={2017}, month={Jun}, pages={715–719} }
 @article{huang_ni_ditto_spano_carney_lai_2017, title={Detecting and characterizing high-frequency oscillations in epilepsy: a case study of big data analysis}, volume={4}, ISSN={2054-5703 2054-5703}, url={http://dx.doi.org/10.1098/rsos.160741}, DOI={10.1098/rsos.160741}, abstractNote={We develop a framework to uncover and analyse dynamical anomalies from massive, nonlinear and non-stationary time series data. The framework consists of three steps: preprocessing of massive datasets to eliminate erroneous data segments, application of the empirical mode decomposition and Hilbert transform paradigm to obtain the fundamental components embedded in the time series at distinct time scales, and statistical/scaling analysis of the components. As a case study, we apply our framework to detecting and characterizing high-frequency oscillations (HFOs) from a big database of rat electroencephalogram recordings. We find a striking phenomenon: HFOs exhibit on–off intermittency that can be quantified by algebraic scaling laws. Our framework can be generalized to big data-related problems in other fields such as large-scale sensor data and seismic data analysis.}, number={1}, journal={Royal Society Open Science}, publisher={The Royal Society}, author={Huang, Liang and Ni, Xuan and Ditto, William L. and Spano, Mark and Carney, Paul R. and Lai, Ying-Cheng}, year={2017}, month={Jan}, pages={160741} }
 @article{kia_lindner_ditto_2017, title={Dynamical coupling outperforms "majority wins" in organizing redundancy to mitigate noise}, volume={87}, ISSN={["1573-269X"]}, DOI={10.1007/s11071-016-3063-z}, number={1}, journal={NONLINEAR DYNAMICS}, author={Kia, Behnam and Lindner, John F. and Ditto, William L.}, year={2017}, month={Jan}, pages={605–615} }
 @article{kohar_kia_lindner_ditto_2017, title={Implementing Boolean Functions in Hybrid Digital-Analog Systems}, volume={7}, ISSN={["2331-7019"]}, DOI={10.1103/physrevapplied.7.044006}, abstractNote={As Moore's Law winds down, we look to do more with less---more computing with fewer components, that is. One approach is ``chaos computing'', in which nonlinear dynamics is exploited to create any type of logic gate on the fly, almost instantly, from a single generic setup. Starting from super-stable initial conditions robust to noise, the authors combine a conventional digital circuit with an analog nonlinear circuit of just three transistors, to implement arbitrary Boolean functions $e\phantom{\rule{0}{0ex}}x\phantom{\rule{0}{0ex}}p\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}y$ faster than in prior architectures. This improves the reliability of chaos-based systems, and expands the scope of their potential applications.}, number={4}, journal={PHYSICAL REVIEW APPLIED}, author={Kohar, Vivek and Kia, Behnam and Lindner, John F. and Ditto, William L.}, year={2017}, month={Apr} }
 @inproceedings{kia_ditto_2017, title={Nonlinear dynamics and chaos for fleixble, reconfigurable computing}, DOI={10.1109/icrc.2017.8123679}, abstractNote={Nonlinear dynamics and chaos contribute flexibility and rich, complex behavior to nonlinear systems. Transistors and transistor circuits are inherently nonlinear. It was demonstrated that this nonlinearity and the flexibility that comes with it can be utilized to implement flexible, reconfigurable computing, and such approaches are called Nonlinear Dynamics-Based Computing. In nonlinear dynamics-based computing, a very same circuit can be reprogrammed to implement and perform many different types of computations, thereby increasing the amount of computing that can be obtained per transistor. For example, at the gate level, the same transistor circuit can implement all different logical gates, such as AND gate or XOR gate. Or at the system level, the same transistor circuit can implement a variety of different higher-level functions, such as addition or subtraction. Another remarkable feature of nonlinear dynamics-based computing is that because different types of functions or operations coexist within the dynamics of the circuit, reprograming and reconfiguring is nearly instant. A recently fabricated VLSI chip for nonlinear dynamics-based computing was shown to be capable of implementing a new function in each clock cycle, with no need for separate reprograming time in between clock cycles. In this paper we briefly review this new approach to computing, present some of our latest results, discuss the implications and possible advantages of nonlinear dynamics-based computing, and plot potential horizons for this exciting new approach to computing.}, booktitle={2017 IEEE International Conference on Rebooting Computing (ICRC)}, author={Kia, B. and Ditto, William}, year={2017}, pages={282–289} }
 @article{kia_lindner_ditto_2017, title={Nonlinear dynamics as an engine of computation}, volume={375}, ISSN={1364-503X 1471-2962}, url={http://dx.doi.org/10.1098/rsta.2016.0222}, DOI={10.1098/rsta.2016.0222}, abstractNote={Control of chaos teaches that control theory can tame the complex, random-like behaviour of chaotic systems. This alliance between control methods and physics—cybernetical physics—opens the door to many applications, including dynamics-based computing. In this article, we introduce nonlinear dynamics and its rich, sometimes chaotic behaviour as an engine of computation. We review our work that has demonstrated how to compute using nonlinear dynamics. Furthermore, we investigate the interrelationship between invariant measures of a dynamical system and its computing power to strengthen the bridge between physics and computation. This article is part of the themed issue ‘Horizons of cybernetical physics’.}, number={2088}, journal={Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences}, publisher={The Royal Society}, author={Kia, Behnam and Lindner, John F. and Ditto, William L.}, year={2017}, month={Mar}, pages={20160222} }
 @inproceedings{kia_parnami_mendes_ditto_2017, title={Nonlinear dynamics-based adaptive hardware}, DOI={10.1109/ahs.2017.8046379}, abstractNote={In this paper we briefly review some recent results in the field of nonlinear dynamics-based computing and how it can be utilized to implement flexible, reprogrammable hardware. Then we propose that such internal flexibility can be utilized to compensate for the negative effects of both internal and external changes. More specifically, we report results of an experimental study that we performed on an integrated circuit fabricated for nonlinear dynamics-based computing, where we overheated the circuit to a point that its operation and performance changed, but then we reprogramed the circuit so that the overheated circuit could again perform the same operations reliably. This inherent flexibility and reprogrammability opens the door to implementing adaptive circuits and systems that can withstand both variable environments and adverse conditions.}, booktitle={2017 nasa/esa conference on adaptive hardware and systems (ahs)}, author={Kia, B. and Parnami, A. and Mendes, A. and Ditto, William}, year={2017}, pages={200–205} }
 @inbook{kia_kohar_ditto_2017, title={Present and the Future of Chaos Computing}, ISBN={9783319526201 9783319526218}, ISSN={2367-3370 2367-3389}, url={http://dx.doi.org/10.1007/978-3-319-52621-8_9}, DOI={10.1007/978-3-319-52621-8_9}, abstractNote={We study chaos computing as a new approach for reconfigurable computing and present some of our latest results and discuss what this new direction to computing means and implies. We discuss the advantages and challenges that come with this new paradigm of computing and envision its future.}, booktitle={Lecture Notes in Networks and Systems}, publisher={Springer International Publishing}, author={Kia, Behnam and Kohar, Vivek and Ditto, William}, year={2017}, pages={101–109} }
 @inproceedings{kia_kohar_ditto_2017, title={Present and the future of chaos computing}, volume={6}, booktitle={Proceedings of the 4th international conference on applications in nonlinear dynamics (icand 2016)}, author={Kia, B. and Kohar, V. and Ditto, W.}, year={2017}, pages={101–109} }
 @inbook{kohar_lindner_kia_ditto_2017, title={Spectral Scaling Analysis of RR Lyrae Stars in OGLE-IV Galactic Bulge Fields}, ISBN={9783319526201 9783319526218}, ISSN={2367-3370 2367-3389}, url={http://dx.doi.org/10.1007/978-3-319-52621-8_6}, DOI={10.1007/978-3-319-52621-8_6}, abstractNote={Recent studies of variable stars have uncovered characteristic nonlinear features in flux of these stars and indicate the presence of quasiperiodicity. A common technique to study quasiperiodic systems is spectral scaling analysis which relies on the fact that different dynamical behaviors can be identified on the basis of distribution of peaks in the periodogram. Here we apply the spectral scaling technique to the OGLE-IV photometry of the RR Lyrae stars in the Galactic bulge. We find that spectra of the fundamental mode (RRab) and first overtone RR Lyrae stars (RRc) scales differently and thus the spectral scaling can be used to distinguish between different RR Lyrae sub classes. Furthermore, goodness of fit for RRc stars with multiple modes is better than other stars. The scaling exponent for stars observed in high cadence is close to the values reported using Kepler photometry. This analysis can help us to reclassify the stars based on their dynamical characteristics.}, booktitle={Lecture Notes in Networks and Systems}, publisher={Springer International Publishing}, author={Kohar, Vivek and Lindner, John F. and Kia, Behnam and Ditto, William L.}, year={2017}, pages={65–76} }
 @inproceedings{kohar_lindner_kia_ditto_2017, title={Spectral scaling analysis of RR Lyrae stars in OGLE-IV Galactic Bulge Fields}, volume={6}, booktitle={Proceedings of the 4th international conference on applications in nonlinear dynamics (icand 2016)}, author={Kohar, V. and Lindner, J. F. and Kia, B. and Ditto, W. L.}, year={2017}, pages={65–76} }
 @article{kia_lindner_ditto_2016, title={A Simple Nonlinear Circuit Contains an Infinite Number of Functions}, volume={63}, ISSN={["1558-3791"]}, DOI={10.1109/tcsii.2016.2538358}, abstractNote={The complex dynamics of a simple nonlinear circuit contains an infinite number of functions. Specifically, this brief shows that the number of different functions that a nonlinear or chaotic circuit can implement exponentially increases as the circuit evolves in time, and this exponential increase is quantified with an exponent that is named the computing exponent. This brief argues that a simple nonlinear circuit that illustrates rich complex dynamics can embody infinitely many different functions, each of which can be dynamically selected. In practice, not all of these functions may be accessible due to factors such as noise or instability of the functions. However, these infinitely many functions do exist within the dynamics of the nonlinear circuit regardless of accessibility or inaccessibility of the functions in practice. This nonlinear-dynamics-based approach to computation opens the door for implementing extremely slim low-power circuits that are capable of performing many different types of functions.}, number={10}, journal={IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS}, author={Kia, Behnam and Lindner, John F. and Ditto, William L.}, year={2016}, month={Oct}, pages={944–948} }
 @article{kohar_kia_lindner_ditto_2016, title={Reduction of Additive Colored Noise Using Coupled Dynamics}, volume={26}, ISSN={0218-1274 1793-6551}, url={http://dx.doi.org/10.1142/s021812741650005x}, DOI={10.1142/s021812741650005x}, abstractNote={We study the effect of additive colored noise on the evolution of maps and demonstrate that the deviations caused by such noise can be reduced using coupled dynamics. We consider both Ornstein–Uhlenbeck process as well as [Formula: see text] noise in our numerical simulations. We observe that though the variance of deviations caused by noise depends on the correlations in the noise, under optimal coupling strength, it decreases by a factor equal to the number of coupled elements in the array as compared to the variance of deviations in a single isolated map. This reduction in noise levels occurs in chaotic as well as periodic regime of the maps. Lastly, we examine the effect of colored noise in chaos computing and find that coupling the chaos computing elements enhances the robustness of chaos computing.}, number={01}, journal={International Journal of Bifurcation and Chaos}, publisher={World Scientific Pub Co Pte Lt}, author={Kohar, Vivek and Kia, Behnam and Lindner, John F. and Ditto, William L.}, year={2016}, month={Jan}, pages={1650005} }
 @article{kohar_kia_kia_lindner_ditto_2016, title={Role of network topology in noise reduction using coupled dynamics}, volume={84}, ISSN={["1573-269X"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84954519290&partnerID=MN8TOARS}, DOI={10.1007/s11071-016-2607-6}, number={3}, journal={NONLINEAR DYNAMICS}, author={Kohar, Vivek and Kia, Sarvenaz and Kia, Behnam and Lindner, John F. and Ditto, William L.}, year={2016}, month={May}, pages={1805–1812} }
 @article{lindner_kohar_kia_hippke_learned_ditto_2016, title={Simple nonlinear models suggest variable star universality}, volume={316}, ISSN={0167-2789}, url={http://dx.doi.org/10.1016/J.PHYSD.2015.10.006}, DOI={10.1016/j.physd.2015.10.006}, abstractNote={Dramatically improved data from observatories like the CoRoT and Kepler spacecraft have recently facilitated nonlinear time series analysis and phenomenological modeling of variable stars, including the search for strange (aka fractal) or chaotic dynamics. We recently argued [Lindner et al., Phys. Rev. Lett. 114 (2015) 054101] that the Kepler data includes "golden" stars, whose luminosities vary quasiperiodically with two frequencies nearly in the golden ratio, and whose secondary frequencies exhibit power-law scaling with exponent near -1.5, suggesting strange nonchaotic dynamics and singular spectra. Here we use a series of phenomenological models to make plausible the connection between golden stars and fractal spectra. We thereby suggest that at least some features of variable star dynamics reflect universal nonlinear phenomena common to even simple systems.}, journal={Physica D: Nonlinear Phenomena}, publisher={Elsevier BV}, author={Lindner, John F. and Kohar, Vivek and Kia, Behnam and Hippke, Michael and Learned, John G. and Ditto, William L.}, year={2016}, month={Feb}, pages={16–22} }
 @article{kohar_kia_lindner_ditto_2016, title={Superlinearly scalable noise robustness of redundant coupled dynamical systems}, volume={93}, ISSN={["1550-2376"]}, DOI={10.1103/physreve.93.032213}, abstractNote={We illustrate through theory and numerical simulations that redundant coupled dynamical systems can be extremely robust against local noise in comparison to uncoupled dynamical systems evolving in the same noisy environment. Previous studies have shown that the noise robustness of redundant coupled dynamical systems is linearly scalable and deviations due to noise can be minimized by increasing the number of coupled units. Here, we demonstrate that the noise robustness can actually be scaled superlinearly if some conditions are met and very high noise robustness can be realized with very few coupled units. We discuss these conditions and show that this superlinear scalability depends on the nonlinearity of the individual dynamical units. The phenomenon is demonstrated in discrete as well as continuous dynamical systems. This superlinear scalability not only provides us an opportunity to exploit the nonlinearity of physical systems without being bogged down by noise but may also help us in understanding the functional role of coupled redundancy found in many biological systems. Moreover, engineers can exploit superlinear noise suppression by starting a coupled system near (not necessarily at) the appropriate initial condition.}, number={3}, journal={PHYSICAL REVIEW E}, author={Kohar, Vivek and Kia, Behnam and Lindner, John F. and Ditto, William L.}, year={2016}, month={Mar} }
 @article{kia_kia_lindner_sinha_ditto_2015, title={Coupling reduces noise: Applying dynamical coupling to reduce local white additive noise}, volume={25}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84928522325&partnerID=MN8TOARS}, DOI={10.1142/S0218127415500406}, abstractNote={We demonstrate how coupling nonlinear dynamical systems can reduce the effects of noise. For simplicity we investigate noisy coupled map lattices. Noise from different lattice nodes can diffuse across the lattice and lower the noise level of individual nodes. We develop a theoretical model that explains this observed noise evolution and show how the coupled dynamics can naturally function as an averaging filter. Our numerical simulations are in excellent agreement with the model predictions.}, number={3}, journal={International Journal of Bifurcation and Chaos}, author={Kia, B. and Kia, S. and Lindner, J.F. and Sinha, S. and Ditto, W.L.}, year={2015} }
 @article{ditto_sinha_2015, title={Exploiting chaos for applications}, volume={25}, ISSN={1054-1500 1089-7682}, url={http://dx.doi.org/10.1063/1.4922976}, DOI={10.1063/1.4922976}, abstractNote={We discuss how understanding the nature of chaotic dynamics allows us to control these systems. A controlled chaotic system can then serve as a versatile pattern generator that can be used for a range of application. Specifically, we will discuss the application of controlled chaos to the design of novel computational paradigms. Thus, we present an illustrative research arc, starting with ideas of control, based on the general understanding of chaos, moving over to applications that influence the course of building better devices.}, number={9}, journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, publisher={AIP Publishing}, author={Ditto, William L. and Sinha, Sudeshna}, year={2015}, month={Sep}, pages={097615} }
 @article{kia_lindner_ditto_2015, title={Nonlinear dynamics based digital logic and circuits}, volume={9}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84930614116&partnerID=MN8TOARS}, DOI={10.3389/fncom.2015.00049}, abstractNote={We discuss the role and importance of dynamics in the brain and biological neural networks and argue that dynamics is one of the main missing elements in conventional Boolean logic and circuits. We summarize a simple dynamics based computing method, and categorize different techniques that we have introduced to realize logic, functionality, and programmability. We discuss the role and importance of coupled dynamics in networks of biological excitable cells, and then review our simple coupled dynamics based method for computing. In this paper, for the first time, we show how dynamics can be used and programmed to implement computation in any given base, including but not limited to base two.}, number={MAY}, journal={Frontiers in Computational Neuroscience}, author={Kia, B. and Lindner, J.F. and Ditto, W.L.}, year={2015} }
 @article{lindner_kohar_kia_hippke_learned_ditto_2015, title={Strange nonchaotic stars}, volume={114}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84922388274&partnerID=MN8TOARS}, DOI={10.1103/PhysRevLett.114.054101}, abstractNote={The unprecedented light curves of the Kepler space telescope document how the brightness of some stars pulsates at primary and secondary frequencies whose ratios are near the golden mean, the most irrational number. A nonlinear dynamical system driven by an irrational ratio of frequencies generically exhibits a strange but nonchaotic attractor. For Kepler's "golden" stars, we present evidence of the first observation of strange nonchaotic dynamics in nature outside the laboratory. This discovery could aid the classification and detailed modeling of variable stars.}, number={5}, journal={Physical Review Letters}, author={Lindner, J.F. and Kohar, V. and Kia, B. and Hippke, M. and Learned, J.G. and Ditto, W.L.}, year={2015} }
 @inbook{ditto_miliotis_murali_sinha_2014, place={Beijing}, series={Applied mathematics, OT}, title={Logic from Dynamics}, ISBN={9781611973259}, booktitle={Chaotic Signal Processing}, publisher={Higher Education Press}, author={Ditto, William L. and Miliotis, Abraham and Murali, K. and Sinha, Sudeshna}, editor={Leung, HenryEditor}, year={2014}, pages={102–127}, collection={Applied mathematics, OT} }
 @article{kia_kia_lindner_sinha_ditto_2014, title={Noise tolerant spatiotemporal chaos computing}, volume={24}, ISSN={1054-1500 1089-7682}, url={http://dx.doi.org/10.1063/1.4897168}, DOI={10.1063/1.4897168}, abstractNote={We introduce and design a noise tolerant chaos computing system based on a coupled map lattice (CML) and the noise reduction capabilities inherent in coupled dynamical systems. The resulting spatiotemporal chaos computing system is more robust to noise than a single map chaos computing system. In this CML based approach to computing, under the coupled dynamics, the local noise from different nodes of the lattice diffuses across the lattice, and it attenuates each other's effects, resulting in a system with less noise content and a more robust chaos computing architecture.}, number={4}, journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, publisher={AIP Publishing}, author={Kia, Behnam and Kia, Sarvenaz and Lindner, John F. and Sinha, Sudeshna and Ditto, William L.}, year={2014}, month={Dec}, pages={043110} }
 @article{hippke_learned_zee_edmondson_lindner_kia_ditto_stevens_2014, title={Pulsation Period Variations in the RRc Lyrae Star KIC 5520878}, volume={798}, ISSN={1538-4357}, url={http://dx.doi.org/10.1088/0004-637X/798/1/42}, DOI={10.1088/0004-637X/798/1/42}, abstractNote={Learned et. al. proposed that a sufficiently advanced extra-terrestrial civilization may tickle Cepheid and RR Lyrae variable stars with a neutrino beam at the right time, thus causing them to trigger early and jogging the otherwise very regular phase of their expansion and contraction. This would turn these stars into beacons to transmit information throughout the galaxy and beyond. The idea is to search for signs of phase modulation (in the regime of short pulse duration) and patterns, which could be indicative of intentional, omnidirectional signaling. We have performed such a search among variable stars using photometric data from the Kepler space telescope. In the RRc Lyrae star KIC 5520878, we have found two such regimes of long and short pulse durations. The sequence of period lengths, expressed as time series data, is strongly auto correlated, with correlation coefficients of prime numbers being significantly higher ($p=99.8$\%). Our analysis of this candidate star shows that the prime number oddity originates from two simultaneous pulsation periods and is likely of natural origin. Simple physical models elucidate the frequency content and asymmetries of the KIC 5520878 light curve. Despite this SETI null result, we encourage testing other archival and future time-series photometry for signs of modulated stars. This can be done as a by-product to the standard analysis, and even partly automated.}, number={1}, journal={The Astrophysical Journal}, publisher={IOP Publishing}, author={Hippke, Michael and Learned, John G. and Zee, A. and Edmondson, William H. and Lindner, John F. and Kia, Behnam and Ditto, William L. and Stevens, Ian R.}, year={2014}, month={Dec}, pages={42} }
 @inbook{kia_murali_jahed motlagh_sinha_ditto_2014, place={Cham, Switzerland}, title={Synthetic Computation: Chaos Computing, Logical Stochastic Resonance, and Adaptive Computing}, ISBN={9783319029245 9783319029252}, ISSN={1860-0832 1860-0840}, url={http://dx.doi.org/10.1007/978-3-319-02925-2_5}, DOI={10.1007/978-3-319-02925-2_5}, abstractNote={Nonlinearity and chaos can illustrate numerous behaviors and patterns, and one can select different patterns from this rich library of patterns. In this paper we focus on synthetic computing, a field that engineers and synthesizes nonlinear systems to obtain computation. We explain the importance of nonlinearity, and describe how nonlinear systems can be engineered to perform computation. More specifically, we provide an overview of chaos computing, a field that manually programs chaotic systems to build different types of digital functions. Also we briefly describe logical stochastic resonance (LSR), and then extend the approach of LSR to realize combinational digital logic systems via suitable concatenation of existing logical stochastic resonance blocks. Finally we demonstrate how a chaotic system can be engineered and mated with different machine learning techniques, such as artificial neural networks, random searching, and genetic algorithm, to design different autonomous systems that can adapt and respond to environmental conditions.}, booktitle={International Conference on Theory and Application in Nonlinear Dynamics (ICAND 2012). Understanding Complex Systems}, publisher={Springer International Publishing}, author={Kia, Behnam and Murali, K. and Jahed Motlagh, Mohammad-Reza and Sinha, Sudeshna and Ditto, William L.}, editor={Palacios, V. A. and Longhini, P.Editors}, year={2014}, pages={51–65} }
 @article{kia_lindner_ditto_2014, title={Watch your step: Integrating nonlinear dynamical flows by stepping through space and time}, volume={24}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84928336406&partnerID=MN8TOARS}, DOI={10.1142/S0218127414501454}, abstractNote={Nonlinear dynamical flows are often solved approximately by numerical integration based on advancing the independent variable, typically time. Here, we present a unified framework for numerical integration of differential equations based on advancing either the dependent variable, often space, or the independent variable, or any combination of the two. Spacetime stepping unifies and extends previous work. In particular, dependent variable stepping can produce better numerical results and also more faithfully describe the underlying physics, thereby providing both practical and conceptual benefits. We indicate extensions to higher dimensions.}, number={11}, journal={International Journal of Bifurcation and Chaos}, author={Kia, B. and Lindner, J.F. and Ditto, W.L.}, year={2014} }
 @article{stanley_talathi_parekh_cordiner_zhou_mareci_ditto_carney_2013, title={Phase shift in the 24-hour rhythm of hippocampal EEG spiking activity in a rat model of temporal lobe epilepsy}, volume={110}, ISSN={0022-3077 1522-1598}, url={http://dx.doi.org/10.1152/jn.00911.2012}, DOI={10.1152/jn.00911.2012}, abstractNote={For over a century epileptic seizures have been known to cluster at specific times of the day. Recent studies have suggested that the circadian regulatory system may become permanently altered in epilepsy, but little is known about how this affects neural activity and the daily pattern of seizures. To investigate, we tracked long-term changes in the rate of spontaneous hippocampal EEG spikes (SPKs) in a rat model of temporal lobe epilepsy. In healthy animals, SPKs oscillated with near 24-h period; however, after injury by status epilepticus, a persistent phase shift of ∼12 h emerged in animals that later went on to develop chronic spontaneous seizures. Additional measurements showed that global 24-h rhythms, including core body temperature and theta state transitions, did not phase shift. Instead, we hypothesized that locally impaired circadian input to the hippocampus might be responsible for the SPK phase shift. This was investigated with a biophysical computer model in which we showed that subtle changes in the relative strengths of circadian input could produce a phase shift in hippocampal neural activity. MRI provided evidence that the medial septum, a putative circadian relay center for the hippocampus, exhibits signs of damage and therefore could contribute to local circadian impairment. Our results suggest that balanced circadian input is critical to maintaining natural circadian phase in the hippocampus and that damage to circadian relay centers, such as the medial septum, may disrupt this balance. We conclude by discussing how abnormal circadian regulation may contribute to the daily rhythms of epileptic seizures and related cognitive dysfunction.}, number={5}, journal={Journal of Neurophysiology}, publisher={American Physiological Society}, author={Stanley, David A. and Talathi, Sachin S. and Parekh, Mansi B. and Cordiner, Daniel J. and Zhou, Junli and Mareci, Thomas H. and Ditto, William L. and Carney, Paul R.}, year={2013}, month={Sep}, pages={1070–1086} }
 @article{kia_spano_ditto_2011, title={Chaos computing in terms of periodic orbits}, volume={84}, ISSN={1539-3755 1550-2376}, url={http://dx.doi.org/10.1103/PhysRevE.84.036207}, DOI={10.1103/PhysRevE.84.036207}, abstractNote={The complex dynamics of chaotic systems can perform computations. The parameters and/or the initial conditions of a dynamical system are the data inputs and the resulting system state is the output of the computation. By controlling how inputs are mapped to outputs, a specific function can be performed. Previously no clear connection has been drawn between the structure of the dynamics and the computation. In this paper we demonstrate how chaos computation can be explained, modeled, and even predicted in terms of the dynamics of the underlying chaotic system, specifically the periodic orbit structure of the system. Knowing the dynamical equations of the system, we compute the system's periodic orbits as well as its stability in terms of its eigenvalues, thereby demonstrating how, how well, and what the chaotic system can compute.}, number={3}, journal={Physical Review E}, publisher={American Physical Society (APS)}, author={Kia, Behnam and Spano, Mark L. and Ditto, William L.}, year={2011}, month={Sep} }
 @inbook{kia_ditto_spano_2011, title={Chaos for Speech Coding and Production}, volume={7015 LNAI}, ISBN={9783642250194 9783642250200}, ISSN={0302-9743 1611-3349}, url={http://dx.doi.org/10.1007/978-3-642-25020-0_35}, DOI={10.1007/978-3-642-25020-0_35}, abstractNote={The presence of nonlinearity and chaotic behavior in the human speech production system has been reported previously; however to date chaotic dynamics has not been widely exploited in speech coding and artificial speech production algorithms. In this paper we illustrate how we can utilize chaotic dynamics in speech coding and synthesis and discuss how it can improve the performance of these processes. As an example we choose code-excited linear predictive coding and, instead of an excitation codebook consisting of Gaussian random waveforms, we use chaotic systems to produce chaotic excitations. This simple technique has the potential to greatly improve the efficiency of modern communication devices such as cell phones. We call the resulting scheme chaos-excited linear predictive coding.}, booktitle={Advances in Nonlinear Speech Processing}, publisher={Springer Berlin Heidelberg}, author={Kia, Behnam and Ditto, William L. and Spano, Mark L.}, year={2011}, pages={270–278} }
 @inbook{carney_talathi_hwang_ditto_2011, title={Circadian Regulation of Neural Excitability in Temporal Lobe Epilepsy}, ISBN={9781439838853 9781439838860}, url={http://dx.doi.org/10.1201/b10866-24}, DOI={10.1201/b10866-24}, booktitle={Epilepsy}, publisher={CRC Press}, author={Carney, Paul and Talathi, Sachin and Hwang, Dong-Uk and Ditto, William}, year={2011}, month={May}, pages={289–306} }
 @article{dari_kia_bulsara_ditto_2011, title={Creating morphable logic gates using logical stochastic resonance in an engineered gene network}, volume={93}, ISSN={0295-5075 1286-4854}, url={http://dx.doi.org/10.1209/0295-5075/93/18001}, DOI={10.1209/0295-5075/93/18001}, abstractNote={A method for providing a biological logic gate comprising the following steps: subjecting a bistable autoregulatory gene network (GRN) to a noisy background; identifying adjustable parameters of the GRN; using logical stochastic resonance to determine values of the GRN parameters which result in the GRN performing different logic gate functions; and setting the parameter values of the GRN such that the GRN performs a first logic gate function.}, number={1}, journal={EPL (Europhysics Letters)}, publisher={IOP Publishing}, author={Dari, Anna and Kia, Behnam and Bulsara, Adi R. and Ditto, William}, year={2011}, month={Jan}, pages={18001} }
 @article{dari_kia_bulsara_ditto_2011, title={Logical stochastic resonance with correlated internal and external noises in a synthetic biological logic block}, volume={21}, ISSN={1054-1500 1089-7682}, url={http://dx.doi.org/10.1063/1.3660159}, DOI={10.1063/1.3660159}, abstractNote={Following the advent of synthetic biology, several gene networks have been engineered to emulate digital devices, with the ability to program cells for different applications. In this work, we adapt the concept of logical stochastic resonance to a synthetic gene network derived from a bacteriophage λ. The intriguing results of this study show that it is possible to build a biological logic block that can emulate or switch from the AND to the OR gate functionalities through externally tuning the system parameters. Moreover, this behavior and the robustness of the logic gate are underpinned by the presence of an optimal amount of random fluctuations. We extend our earlier work in this field, by taking into account the effects of correlated external (additive) and internal (multiplicative or state-dependent) noise. Results obtained through analytical calculations as well as numerical simulations are presented.}, number={4}, journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, publisher={AIP Publishing}, author={Dari, Anna and Kia, Behnam and Bulsara, Adi R. and Ditto, William L.}, year={2011}, month={Dec}, pages={047521} }
 @inproceedings{murali_sinha_bulsara_dari_ditto_2011, title={Noise enhanced logic gates}, volume={1339}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-79955841975&partnerID=MN8TOARS}, DOI={10.1063/1.3574845}, abstractNote={It was observed recently that, when one drives a two‐state system with two square wave as input, the response of the system mirrors a logical output (NOR/OR). The probability of obtaining the correct logic response is controlled by the interplay between the noise‐floor and the nonlinearity. As one increases the noise intensity, the probability of the output reflecting a NOR/OR operation increases to unity in a window of moderate noise, and then decreases to zero again for very large noise. This concept of noise enhanced logic gate performance under optimal noise was called: Logical Stochastic Resonance (LSR). Here we review this concept of Logical Stochastic Resonance and provide details of suitable electronic circuit systems demonstrating LSR. We also review the extension of this approach to realize logic gates with Coherence Resonance Systems (LCR).}, booktitle={AIP Conference Proceedings}, author={Murali, K. and Sinha, S. and Bulsara, A.R. and Dari, A. and Ditto, W.L.}, year={2011}, pages={67–77} }
 @article{dari_kia_wang_bulsara_ditto_2011, title={Noise-aided computation within a synthetic gene network through morphable and robust logic gates}, volume={83}, ISSN={1539-3755 1550-2376}, url={http://dx.doi.org/10.1103/PhysRevE.83.041909}, DOI={10.1103/PhysRevE.83.041909}, abstractNote={An important goal for synthetic biology is to build robust and tunable genetic regulatory networks that are capable of performing assigned operations, usually in the presence of noise. In this work, a synthetic gene network derived from the bacteriophage λ underpins a reconfigurable logic gate wherein we exploit noise and nonlinearity through the application of the logical stochastic resonance paradigm. This biological logic gate can emulate or "morph" the AND and OR operations through varying internal system parameters in a noisy background. Such genetic circuits can afford intriguing possibilities in the realization of engineered genetic networks in which the actual function of the gate can be changed after the network has been built, via an external control parameter. In this article, the full system characterization is reported, with the logic gate performance studied in the presence of external and internal noise. The robustness of the gate, to noise, is studied and illustrated through numerical simulations.}, number={4}, journal={Physical Review E}, publisher={American Physical Society (APS)}, author={Dari, Anna and Kia, Behnam and Wang, Xiao and Bulsara, Adi R. and Ditto, William}, year={2011}, month={Apr}, pages={041909} }
 @inproceedings{dari_bulsara_ditto_wang_2011, title={Reprogrammable biological logic gate that exploits noise}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84862923309&partnerID=MN8TOARS}, DOI={10.1109/BioCAS.2011.6107796}, abstractNote={Computation underlies the genetic regulatory network activities. Previous studies have designed and engineered systems that can perform single logic gate functionalities, trying to avoid external and internal random fluctuations. In this work, we demonstrate the possibility to exploit noise when it cannot be eliminated. In particular, we adapt the LSR paradigm to a single-gene network derived from the bacteriophage λ and to a more robust two-gene network derived from the yeast S. cerevisiae. Our results demonstrate that in both cases there is an optimal amount of noise where the biological logic gate can be externally reprogrammed (i.e. switch from the AND to the OR gate) and perform well according to the truth table.}, booktitle={2011 IEEE Biomedical Circuits and Systems Conference, BioCAS 2011}, author={Dari, A. and Bulsara, A.R. and Ditto, W.L. and Wang, X.}, year={2011}, pages={337–340} }
 @article{stanley_bardakjian_spano_ditto_2011, title={Stochastic amplification of calcium-activated potassium currents in Ca2+ microdomains}, volume={31}, ISSN={0929-5313 1573-6873}, url={http://dx.doi.org/10.1007/s10827-011-0328-x}, DOI={10.1007/s10827-011-0328-x}, number={3}, journal={Journal of Computational Neuroscience}, publisher={Springer Science and Business Media LLC}, author={Stanley, David Arthur and Bardakjian, Berj L. and Spano, Mark L. and Ditto, William L.}, year={2011}, month={May}, pages={647–666} }
 @article{kia_dari_ditto_spano_2011, title={Unstable periodic orbits and noise in chaos computing}, volume={21}, ISSN={1054-1500 1089-7682}, url={http://dx.doi.org/10.1063/1.3664349}, DOI={10.1063/1.3664349}, abstractNote={Different methods to utilize the rich library of patterns and behaviors of a chaotic system have been proposed for doing computation or communication. Since a chaotic system is intrinsically unstable and its nearby orbits diverge exponentially from each other, special attention needs to be paid to the robustness against noise of chaos-based approaches to computation. In this paper unstable periodic orbits, which form the skeleton of any chaotic system, are employed to build a model for the chaotic system to measure the sensitivity of each orbit to noise, and to select the orbits whose symbolic representations are relatively robust against the existence of noise. Furthermore, since unstable periodic orbits are extractable from time series, periodic orbit-based models can be extracted from time series too. Chaos computing can be and has been implemented on different platforms, including biological systems. In biology noise is always present; as a result having a clear model for the effects of noise on any given biological implementation has profound importance. Also, since in biology it is hard to obtain exact dynamical equations of the system under study, the time series techniques we introduce here are of critical importance.}, number={4}, journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, publisher={AIP Publishing}, author={Kia, Behnam and Dari, Anna and Ditto, William L. and Spano, Mark L.}, year={2011}, month={Dec}, pages={047520} }
 @article{guerra_bulsara_ditto_sinha_murali_mohanty_2010, title={A Noise-Assisted Reprogrammable Nanomechanical Logic Gate}, volume={10}, ISSN={1530-6984 1530-6992}, url={http://dx.doi.org/10.1021/nl9034175}, DOI={10.1021/nl9034175}, abstractNote={We present a nanomechanical device, operating as a reprogrammable logic gate, and performing fundamental logic functions such as AND/OR and NAND/NOR. The logic function can be programmed (e.g., from AND to OR) dynamically, by adjusting the resonator’s operating parameters. The device can access one of two stable steady states, according to a specific logic function; this operation is mediated by the noise floor which can be directly adjusted, or dynamically “tuned” via an adjustment of the underlying nonlinearity of the resonator, i.e., it is not necessary to have direct control over the noise floor. The demonstration of this reprogrammable nanomechanical logic gate affords a path to the practical realization of a new generation of mechanical computers.}, number={4}, journal={Nano Letters}, publisher={American Chemical Society (ACS)}, author={Guerra, Diego N. and Bulsara, Adi R. and Ditto, William L. and Sinha, Sudeshna and Murali, K. and Mohanty, P.}, year={2010}, month={Apr}, pages={1168–1171} }
 @article{ditto_miliotis_murali_sinha_spano_2010, title={Chaogates: Morphing logic gates that exploit dynamical patterns}, volume={20}, ISSN={1054-1500 1089-7682}, url={http://dx.doi.org/10.1063/1.3489889}, DOI={10.1063/1.3489889}, abstractNote={Chaotic systems can yield a wide variety of patterns. Here we use this feature to generate all possible fundamental logic gate functions. This forms the basis of the design of a dynamical computing device, a chaogate, that can be rapidly morphed to become any desired logic gate. Here we review the basic concepts underlying this and present an extension of the formalism to include asymmetric logic functions.}, number={3}, journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, publisher={AIP Publishing}, author={Ditto, William L. and Miliotis, A. and Murali, K. and Sinha, Sudeshna and Spano, Mark L.}, year={2010}, month={Sep}, pages={037107} }
 @article{fisher_talathi_carney_ditto_2010, title={Effects of phase on homeostatic spike rates}, volume={102}, ISSN={0340-1200 1432-0770}, url={http://dx.doi.org/10.1007/s00422-010-0376-8}, DOI={10.1007/s00422-010-0376-8}, number={5}, journal={Biological Cybernetics}, publisher={Springer Science and Business Media LLC}, author={Fisher, Nicholas and Talathi, Sachin S. and Carney, Paul R. and Ditto, William L.}, year={2010}, month={Mar}, pages={427–440} }
 @article{cadotte_demarse_mareci_parekh_talathi_hwang_ditto_ding_carney_2010, title={Granger causality relationships between local field potentials in an animal model of temporal lobe epilepsy}, volume={189}, ISSN={0165-0270}, url={http://dx.doi.org/10.1016/j.jneumeth.2010.03.007}, DOI={10.1016/j.jneumeth.2010.03.007}, abstractNote={An understanding of the in vivo spatial emergence of abnormal brain activity during spontaneous seizure onset is critical to future early seizure detection and closed-loop seizure prevention therapies. In this study, we use Granger causality (GC) to determine the strength and direction of relationships between local field potentials (LFPs) recorded from bilateral microelectrode arrays in an intermittent spontaneous seizure model of chronic temporal lobe epilepsy before, during, and after Racine grade partial onset generalized seizures. Our results indicate distinct patterns of directional GC relationships within the hippocampus, specifically from the CA1 subfield to the dentate gyrus, prior to and during seizure onset. Our results suggest sequential and hierarchical temporal relationships between the CA1 and dentate gyrus within and across hippocampal hemispheres during seizure. Additionally, our analysis suggests a reversal in the direction of GC relationships during seizure, from an abnormal pattern to more anatomically expected pattern. This reversal correlates well with the observed behavioral transition from tonic to clonic seizure in time-locked video. These findings highlight the utility of GC to reveal dynamic directional temporal relationships between multichannel LFP recordings from multiple brain regions during unprovoked spontaneous seizures.}, number={1}, journal={Journal of Neuroscience Methods}, publisher={Elsevier BV}, author={Cadotte, Alex J. and DeMarse, Thomas B. and Mareci, Thomas H. and Parekh, Mansi B. and Talathi, Sachin S. and Hwang, Dong-Uk and Ditto, William L. and Ding, Mingzhou and Carney, Paul R.}, year={2010}, month={May}, pages={121–129} }
 @article{crutchfield_ditto_sinha_2010, title={Introduction to Focus Issue: Intrinsic and Designed Computation: Information Processing in Dynamical Systems—Beyond the Digital Hegemony}, volume={20}, ISSN={1054-1500 1089-7682}, url={http://dx.doi.org/10.1063/1.3492712}, DOI={10.1063/1.3492712}, abstractNote={How dynamical systems store and process information is a fundamental question that touches a remarkably wide set of contemporary issues: from the breakdown of Moore’s scaling laws—that predicted the inexorable improvement in digital circuitry—to basic philosophical problems of pattern in the natural world. It is a question that also returns one to the earliest days of the foundations of dynamical systems theory, probability theory, mathematical logic, communication theory, and theoretical computer science. We introduce the broad and rather eclectic set of articles in this Focus Issue that highlights a range of current challenges in computing and dynamical systems.}, number={3}, journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, publisher={AIP Publishing}, author={Crutchfield, James P. and Ditto, William L. and Sinha, Sudeshna}, year={2010}, month={Sep}, pages={037101} }
 @article{bulsara_dari_ditto_murali_sinha_2010, title={Logical stochastic resonance}, volume={375}, ISSN={0301-0104}, url={http://dx.doi.org/10.1016/j.chemphys.2010.06.015}, DOI={10.1016/j.chemphys.2010.06.015}, abstractNote={In a recent publication it was shown that, when one drives a two-state system with two square waves as input, the response of the system mirrors a logical output (NOR/OR). The probability of obtaining the correct logic response is controlled by the interplay between the noise-floor and the nonlinearity. As one increases the noise intensity, the probability of the output reflecting a NOR/OR operation increases to unity and then decreases. Varying the nonlinearity (or the thresholds) of the system allows one to morph the output into another logic operation (NAND/AND) whose probability displays analogous behavior. Thus, the outcome of the interplay of nonlinearity and noise is a flexible logic gate with enhanced performance. Here we review this concept of “Logical Stochastic Resonance” (LSR) and provide details of an electronic circuit system demonstrating LSR. Our proof-of-principle experiment involves a particularly simple realization of a two-state system realized by two adjustable thresholds. We also review CMOS implementations of a simple LSR circuit, and the concatenation of these LSR modules to emulate combinational logic, such as data flip-flop and full adder operations.}, number={2-3}, journal={Chemical Physics}, publisher={Elsevier BV}, author={Bulsara, Adi R. and Dari, Anna and Ditto, William L. and Murali, K. and Sinha, Sudeshna}, year={2010}, month={Oct}, pages={424–434} }
 @article{nandan_talathi_myers_ditto_khargonekar_carney_2010, title={Support vector machines for seizure detection in an animal model of chronic epilepsy}, volume={7}, ISSN={1741-2560 1741-2552}, url={http://dx.doi.org/10.1088/1741-2560/7/3/036001}, DOI={10.1088/1741-2560/7/3/036001}, abstractNote={We compare the performance of three support vector machine (SVM) types: weighted SVM, one-class SVM and support vector data description (SVDD) for the application of seizure detection in an animal model of chronic epilepsy. Large EEG datasets (273 h and 91 h respectively, with a sampling rate of 1 kHz) from two groups of rats with chronic epilepsy were used in this study. For each of these EEG datasets, we extracted three energy-based seizure detection features: mean energy, mean curve length and wavelet energy. Using these features we performed twofold cross-validation to obtain the performance statistics: sensitivity (S), specificity (K) and detection latency (tau) as a function of control parameters for the given SVM. Optimal control parameters for each SVM type that produced the best seizure detection statistics were then identified using two independent strategies. Performance of each SVM type is ranked based on the overall seizure detection performance through an optimality index metric (O). We found that SVDD not only performed better than the other SVM types in terms of highest value of the mean optimality index metric (O⁻) but also gave a more reliable performance across the two EEG datasets.}, number={3}, journal={Journal of Neural Engineering}, publisher={IOP Publishing}, author={Nandan, Manu and Talathi, Sachin S and Myers, Stephen and Ditto, William L and Khargonekar, Pramod P and Carney, Paul R}, year={2010}, month={Apr}, pages={036001} }
 @article{talathi_hwang_carney_ditto_2010, title={Synchrony with shunting inhibition in a feedforward inhibitory network}, volume={28}, ISSN={0929-5313 1573-6873}, url={http://dx.doi.org/10.1007/s10827-009-0210-2}, DOI={10.1007/s10827-009-0210-2}, abstractNote={Recent experiments have shown that GABAA receptor mediated inhibition in adult hippocampus is shunting rather than hyperpolarizing. Simulation studies of realistic interneuron networks with strong shunting inhibition have been demonstrated to exhibit robust gamma band (20–80 Hz) synchrony in the presence of heterogeneity in the intrinsic firing rates of individual neurons in the network. In order to begin to understand how shunting can contribute to network synchrony in the presence of heterogeneity, we develop a general theoretical framework using spike time response curves (STRC’s) to study patterns of synchrony in a simple network of two unidirectionally coupled interneurons (UCI network) interacting through a shunting synapse in the presence of heterogeneity. We derive an approximate discrete map to analyze the dynamics of synchronous states in the UCI network by taking into account the nonlinear contributions of the higher order STRC terms. We show how the approximate discrete map can be used to successfully predict the domain of synchronous 1:1 phase locked state in the UCI network. The discrete map also allows us to determine the conditions under which the two interneurons can exhibit in-phase synchrony. We conclude by demonstrating how the information from the study of the discrete map for the dynamics of the UCI network can give us valuable insight into the degree of synchrony in a larger feed-forward network of heterogeneous interneurons.}, number={2}, journal={Journal of Computational Neuroscience}, publisher={Springer Science and Business Media LLC}, author={Talathi, Sachin S. and Hwang, Dong-Uk and Carney, Paul R. and Ditto, William L.}, year={2010}, month={Feb}, pages={305–321} }
 @inbook{ditto_miliotis_murali_sinha_2010, title={The Chaos Computing Paradigm}, volume={3}, ISBN={9783527630967 9783527409457}, url={http://dx.doi.org/10.1002/9783527630967.ch1}, DOI={10.1002/9783527630967.ch1}, booktitle={Reviews of Nonlinear Dynamics and Complexity}, publisher={Wiley-VCH Verlag GmbH & Co. KGaA}, author={Ditto, William L. and Miliotis, Abraham and Murali, K. and Sinha, Sudeshna}, year={2010}, month={Apr}, pages={1–35} }
 @article{miliotis_murali_sinha_ditto_spano_2009, title={A simple nonlinear dynamical computing device}, volume={42}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-67650033090&partnerID=MN8TOARS}, DOI={10.1016/j.chaos.2009.02.010}, abstractNote={We propose and characterize an iterated map whose nonlinearity has a simple (i.e., minimal) electronic implementation. We then demonstrate explicitly how all the different fundamental logic gates can be implemented and morphed using this nonlinearity. These gates provide the full set of gates necessary to construct a general-purpose, reconfigurable computing device. As an example of how such chaotic computing devices can be exploited, we use an array of these maps to encode data and to process information. Each map can store one of M items, where M is variable and can be large. This nonlinear hardware stores data naturally in different bases or alphabets. We also show how this method of storing information can serve as a preprocessing tool for exact or inexact pattern-matching searches.}, number={2}, journal={Chaos, Solitons and Fractals}, author={Miliotis, A. and Murali, K. and Sinha, S. and Ditto, W.L. and Spano, M.L.}, year={2009}, pages={809–819} }
 @article{komalapriya_romano_thiel_schwarz_kurths_simonotto_furman_ditto_carney_2009, title={Analysis of high-resolution microelectrode EEG recordings in an animal model of spontaneous lmbic seizures}, volume={19}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-67449149141&partnerID=MN8TOARS}, DOI={10.1142/S0218127409023226}, abstractNote={We perform a systematic data analysis on high resolution (0.5–12 kHz) multiarray microelectrode recordings from an animal model of spontaneous limbic epilepsy, to investigate the role of high frequency oscillations and the occurrence of early precursors for seizures. Results of spectral analysis confirm the importance of very high frequency oscillations (even greater than 600 Hz) in normal (healthy) and abnormal (epileptic) hippocampus. Furthermore, we show that the measures of Recurrence Quantification Analysis (RQA) and Recurrence Time Statistics (RTS) are successful in indicating, rather uniquely, the onset of ictal state and the occurrence of some warnings/precursors during the pre-ictal state, in contrast to the linear measures investigated.}, number={2}, journal={International Journal of Bifurcation and Chaos}, author={Komalapriya, C. and Romano, M.C. and Thiel, M. and Schwarz, U. and Kurths, J. and Simonotto, J. and Furman, M. and Ditto, W.L. and Carney, P.R.}, year={2009}, pages={605–617} }
 @article{talathi_hwang_ditto_mareci_sepulveda_spano_carney_2009, title={Circadian control of neural excitability in an animal model of temporal lobe epilepsy}, volume={455}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-63449134207&partnerID=MN8TOARS}, DOI={10.1016/j.neulet.2009.03.057}, abstractNote={We provide experimental evidence for the emerging imbalance in the firing activity of two distinct classes (type 1 and type 2) of population spikes recorded from the hippocampal area CA1 in an animal model of temporal lobe epilepsy. We show that during the latent period of epileptogenesis following status epilepticus inducing brain injury, there is a sustained increase in the firing rate of type 1 population spikes (PS1) with a concurrent decrease in the firing rate of type 2 population spikes (PS2). Both PS1 and PS2 firing rates are observed to follow a circadian rhythm and are in-phase in control rats. Following brain injury there is an abrupt phase shift in the circadian activity of the PS firing rates. We hypothesize that this abrupt phase shift is the underlying cause for the emergence of imbalance in the firing activity of the two PS. We test our hypothesis in the framework of a simple two-dimensional Wilson–Cowan model that describes the interaction between firing activities of populations of excitatory and inhibitory neurons.}, number={2}, journal={Neuroscience Letters}, author={Talathi, S.S. and Hwang, D.-U. and Ditto, W.L. and Mareci, T. and Sepulveda, H. and Spano, M. and Carney, P.R.}, year={2009}, pages={145–149} }
 @book{ditto_sinha_2009, title={Construction of a chaotic computer chip}, volume={2009}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-62849109952&partnerID=MN8TOARS}, DOI={10.1007/978-3-540-85632-0_1}, journal={Understanding Complex Systems}, author={Ditto, W.L. and Sinha, S.}, year={2009}, pages={3–13} }
 @article{murali_miliotis_ditto_sinha_2009, title={Logic from nonlinear dynamical evolution}, volume={373}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-61349141829&partnerID=MN8TOARS}, DOI={10.1016/j.physleta.2009.02.026}, abstractNote={We propose a direct and flexible implementation of logic operations using the dynamical evolution of a nonlinear system. The concept involves the observation of the state of the system at different times to obtain different logic outputs. We explicitly implement the basic NAND, AND, NOR, OR and XOR logic gates, as well as multiple-input XOR and XNOR logic gates. Further we demonstrate how the single dynamical system can do more complex operations such as bit-by-bit addition in just a few iterations.}, number={15}, journal={Physics Letters, Section A: General, Atomic and Solid State Physics}, author={Murali, K. and Miliotis, A. and Ditto, W.L. and Sinha, S.}, year={2009}, pages={1346–1351} }
 @article{talathi_hwang_miliotis_carney_ditto_2009, title={Predicting synchrony in heterogeneous pulse coupled oscillators}, volume={80}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-70349559192&partnerID=MN8TOARS}, DOI={10.1103/PhysRevE.80.021908}, abstractNote={Pulse coupled oscillators (PCOs) represent an ubiquitous model for a number of physical and biological systems. Phase response curves (PRCs) provide a general mathematical framework to analyze patterns of synchrony generated within these models. A general theoretical approach to account for the nonlinear contributions from higher-order PRCs in the generation of synchronous patterns by the PCOs is still lacking. Here, by considering a prototypical example of a PCO network, i.e., two synaptically coupled neurons, we present a general theory that extends beyond the weak-coupling approximation, to account for higher-order PRC corrections in the derivation of an approximate discrete map, the stable fixed point of which can predict the domain of 1:1 phase locked synchronous states generated by the PCO network.}, number={2}, journal={Physical Review E - Statistical, Nonlinear, and Soft Matter Physics}, author={Talathi, S.S. and Hwang, D.-U. and Miliotis, A. and Carney, P.R. and Ditto, W.L.}, year={2009} }
 @inbook{carney_fisher_ditto_geyer_2009, place={Norwood, MA, USA}, title={Quantitative Sleep Monitoring}, booktitle={Quantitative EEG Analysis Methods and Applications}, publisher={Artech House, Inc.}, author={Carney, P.R. and Fisher, N. and Ditto, W.L. and Geyer, J.D.}, editor={Tong, Shanbao and Thakor, Nitish V.Editors}, year={2009} }
 @article{murali_rajamohamed_sinha_ditto_bulsara_2009, title={Realization of reliable and flexible logic gates using noisy nonlinear circuits}, volume={95}, ISSN={0003-6951 1077-3118}, url={http://dx.doi.org/10.1063/1.3245318}, DOI={10.1063/1.3245318}, abstractNote={It was shown recently [Murali et al., Phys. Rev. Lett. 102, 104101 (2009)] that when one presents two square waves as input to a two-state system, the response of the system can produce a logical output (NOR/OR) with a probability controlled by the interplay between the system noise and the nonlinearity (that characterizes the bistable dynamics). One can switch or “morph” the output into another logic operation (NAND/AND) whose probability displays analogous behavior; the switching is accomplished via a controlled symmetry-breaking dc input. Thus, the interplay of nonlinearity and noise yields flexible and reliable logic behavior, and the natural outcome is, effectively, a logic gate. This “logical stochastic resonance” is demonstrated here via a circuit implementation using a linear resistor, a linear capacitor and four CMOS-transistors with a battery to produce a cubiclike nonlinearity. This circuit is simple, robust, and capable of operating in very high frequency regimes; further, its ease of implementation with integrated circuits and nanoelectronic devices should prove very useful in the context of reliable logic gate implementation in the presence of circuit noise.}, number={19}, journal={Applied Physics Letters}, publisher={AIP Publishing}, author={Murali, K. and Rajamohamed, I. and Sinha, Sudeshna and Ditto, William L. and Bulsara, Adi R.}, year={2009}, month={Nov}, pages={194102} }
 @article{pourshaghaghi_kia_ditto_jahed-motlagh_2009, title={Reconfigurable logic blocks based on a chaotic Chua circuit}, volume={41}, ISSN={0960-0779}, url={http://dx.doi.org/10.1016/j.chaos.2007.11.030}, DOI={10.1016/j.chaos.2007.11.030}, abstractNote={To investigate morphable chaotic logic we have constructed, out of discrete circuitry, a chaotic logic block that can morph between all two input, one output logic gates. Additionally, we investigate the sensitivity of such a block to noise and have been able to formulate a method that demonstrates that the chaotic saddles of the inherent chaotic dynamics can be exploited to enhance the robustness of the logic functions with respect to noise.}, number={1}, journal={Chaos, Solitons & Fractals}, publisher={Elsevier BV}, author={Pourshaghaghi, Hamid Reza and Kia, Behnam and Ditto, William and Jahed-Motlagh, Mohammad Reza}, year={2009}, month={Jul}, pages={233–244} }
 @article{murali_sinha_ditto_bulsara_2009, title={Reliable logic circuit elements that exploit nonlinearity in the presence of a noise floor}, volume={102}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-63149093596&partnerID=MN8TOARS}, DOI={10.1103/PhysRevLett.102.104101}, abstractNote={The response of a noisy nonlinear system to deterministic input signals can be enhanced by cooperative phenomena. We show that when one presents two square waves as input to a two-state system, the response of the system can produce a logical output (NOR/OR) with a probability controlled by the noise intensity. As one increases the noise (for fixed threshold or nonlinearity), the probability of the output reflecting a NOR/OR operation increases to unity and then decreases. Changing the nonlinearity (or the thresholds) of the system changes the output into another logic operation (NAND/AND) whose probability displays analogous behavior. The interplay of nonlinearity and noise can yield logic behavior, and the emergent outcome of such systems is a logic gate. This "logical stochastic resonance" is demonstrated via an experimental realization of a two-state system with two (adjustable) thresholds.}, number={10}, journal={Physical Review Letters}, author={Murali, K. and Sinha, S. and Ditto, W.L. and Bulsara, A.R.}, year={2009} }
 @article{rahmani_motlagh_ditto_2009, title={Robust control of spatiotemporal chaos in coupled map lattices}, volume={19}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-70149105790&partnerID=MN8TOARS}, DOI={10.1142/S0218127409023883}, abstractNote={In this paper, a new method for controlling spatiotemporal chaos in discrete-time spatially extended systems modeled by coupled map lattices is proposed. This method is based on quasi-sliding mode using a Lyapunov function. This method enables the system to drive the chaotic motion toward any desired trajectory via a sliding surface in the error space. The controller also guarantees finite time convergence of the state trajectory. The main advantage of this method is its robustness with respect to additive uncertainties and its applicability for all types of coupled map lattices. A diffusively coupled map lattice is used as an example to demonstrate the method. Simulation results reveal the robustness and the effectiveness of the method in controlling spatiotemporal chaos in coupled map lattices.}, number={6}, journal={International Journal of Bifurcation and Chaos}, author={Rahmani, Z. and Motlagh, M.R.J. and Ditto, W.}, year={2009}, pages={2031–2042} }
 @inbook{fisher_talathi_cadotte_myers_ditto_geyer_carney_2009, place={Philadelphia}, edition={1st}, title={Seizure Detection and Monitoring}, booktitle={Reading EEGs: A Practical Approach}, publisher={Lippincott-Williams & Wilkins, Inc}, author={Fisher, N. and Talathi, S. and Cadotte, A. and Myers, S. and Ditto, W. and Geyer, J.D. and Carney, P.R.}, editor={Greenfield, L. John and Geyer, James D. and Carney, Paul R.Editors}, year={2009} }
 @article{cadotte_mareci_demarse_parekh_rajagovindan_ditto_talathi_hwang_carney_2009, title={Temporal lobe epilepsy: Anatomical and effective connectivity}, volume={17}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-67650838217&partnerID=MN8TOARS}, DOI={10.1109/TNSRE.2008.2006220}, abstractNote={While temporal lobe epilepsy (TLE) has been treatable with anti-seizure medications over the past century, there still remain a large percentage of patients whose seizures remain untreatable pharmacologically. To better understand and treat TLE, our laboratory uses several <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vivo</i> analytical techniques to estimate connectivity in epilepsy. This paper reviews two different connectivity-based approaches with an emphasis on application to the study of epilepsy. First, we present effective connectivity techniques, such as Granger causality, that has been used to assess the dynamic directional relationships among brain regions. These measures are used to better understand how seizure activity initiates, propagates, and terminates. Second, structural techniques, such as magnetic resonance imaging, can be used to assess changes in the underlying neural structures that result in seizure. This paper also includes <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vivo</i> epilepsy-centered examples of both effective and anatomical connectivity analysis. These analyses are performed on data collected <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vivo</i> from a spontaneously seizing animal model of TLE. Future work <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vivo</i> on epilepsy will no doubt benefit from a fusion of these different techniques. We conclude by discussing the interesting possibilities, implications, and challenges that a unified analysis would present.}, number={3}, journal={IEEE Transactions on Neural Systems and Rehabilitation Engineering}, author={Cadotte, A.J. and Mareci, T.H. and DeMarse, T.B. and Parekh, M.B. and Rajagovindan, R. and Ditto, W.L. and Talathi, S.S. and Hwang, D.-U. and Carney, P.R.}, year={2009}, pages={214–223} }
 @article{ditto_murali_sinha_2008, title={Chaos computing: Ideas and implementations}, volume={366}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-38149114147&partnerID=MN8TOARS}, DOI={10.1098/rsta.2007.2116}, abstractNote={We review the concept of the ‘chaos computing’ paradigm, which exploits the controlled richness of nonlinear dynamics to obtain flexible reconfigurable hardware. We demonstrate the idea with specific schemes and verify the schemes through proof-of-principle experiments.}, number={1865}, journal={Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences}, author={Ditto, W.L. and Murali, K. and Sinha, S.}, year={2008}, pages={653–664} }
 @book{carney_cadotte_demarse_vemuri_mareci_ditto_2008, title={Effective and Anatomical Connectivity in a Rat Model of Spontaneous Limbic Seizure}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84889476603&partnerID=MN8TOARS}, DOI={10.1002/9783527625192.ch4}, abstractNote={This chapter contains sections titled: Introduction Granger Causality Structural Visualization with Magnetic Resonance Acknowledgments References}, journal={Seizure Prediction in Epilepsy: From Basic Mechanisms to Clinical Applications}, author={Carney, P.R. and Cadotte, A. and Demarse, T.B. and Vemuri, B. and Mareci, T.H. and Ditto, W.}, year={2008}, pages={45–59} }
 @article{miliotis_sinha_ditto_2008, title={Exploiting nonlinear dynamics to store and process information}, volume={18}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-47749092109&partnerID=MN8TOARS}, DOI={10.1142/S0218127408021166}, abstractNote={By applying nonlinear dynamics to the dense storage of information, we demonstrate how a single nonlinear dynamical element can store M items, where M is variable and can be large. This provides the capability for naturally storing data in different bases or in different alphabets and can be used to implement multilevel logic. Further we show how this method of storing information can serve as a preprocessing tool for (exact or inexact) pattern matching searches. Since our scheme involves just a single procedural step, it is naturally set up for parallel implementation and can be realized with hardware currently employed for chaos-based computing architectures.}, number={5}, journal={International Journal of Bifurcation and Chaos}, author={Miliotis, A. and Sinha, S. and Ditto, W.L.}, year={2008}, pages={1551–1559} }
 @article{talathi_hwang_spano_simonotto_furman_myers_winters_ditto_carney_2008, title={Non-parametric early seizure detection in an animal model of temporal lobe epilepsy}, volume={5}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-40549088889&partnerID=MN8TOARS}, DOI={10.1088/1741-2560/5/1/009}, abstractNote={The performance of five non-parametric, univariate seizure detection schemes (embedding delay, Hurst scale, wavelet scale, nonlinear autocorrelation and variance energy) were evaluated as a function of the sampling rate of EEG recordings, the electrode types used for EEG acquisition, and the spatial location of the EEG electrodes in order to determine the applicability of the measures in real-time closed-loop seizure intervention. The criteria chosen for evaluating the performance were high statistical robustness (as determined through the sensitivity and the specificity of a given measure in detecting a seizure) and the lag in seizure detection with respect to the seizure onset time (as determined by visual inspection of the EEG signal by a trained epileptologist). An optimality index was designed to evaluate the overall performance of each measure. For the EEG data recorded with microwire electrode array at a sampling rate of 12 kHz, the wavelet scale measure exhibited better overall performance in terms of its ability to detect a seizure with high optimality index value and high statistics in terms of sensitivity and specificity.}, number={1}, journal={Journal of Neural Engineering}, author={Talathi, S.S. and Hwang, D.-U. and Spano, M.L. and Simonotto, J. and Furman, M.D. and Myers, S.M. and Winters, J.T. and Ditto, W.L. and Carney, P.R.}, year={2008}, pages={85–98} }
 @article{talathi_hwang_ditto_2008, title={Spike timing dependent plasticity promotes synchrony of inhibitory networks in the presence of heterogeneity}, volume={25}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-51349162681&partnerID=MN8TOARS}, DOI={10.1007/s10827-008-0077-7}, abstractNote={Recently Haas et al. (J Neurophysiol 96: 3305–3313, 2006), observed a novel form of spike timing dependent plasticity (iSTDP) in GABAergic synaptic couplings in layer II of the entorhinal cortex. Depending on the relative timings of the presynaptic input at time t pre and the postsynaptic excitation at time t post, the synapse is strengthened (Δt = t post − t pre > 0) or weakened (Δt < 0). The temporal dynamic range of the observed STDP rule was found to lie in the higher gamma frequency band (≥40 Hz), a frequency range important for several vital neuronal tasks. In this paper we study the function of this novel form of iSTDP in the synchronization of the inhibitory neuronal network. In particular we consider a network of two unidirectionally coupled interneurons (UCI) and two mutually coupled interneurons (MCI), in the presence of heterogeneity in the intrinsic firing rates of each coupled neuron. Using the method of spike time response curve (STRC), we show how iSTDP influences the dynamics of the coupled neurons, such that the pair synchronizes under moderately large heterogeneity in the firing rates. Using the general properties of the STRC for a Type-1 neuron model (Ermentrout, Neural Comput 8:979–1001, 1996) and the observed iSTDP we determine conditions on the initial configuration of the UCI network that would result in 1:1 in-phase synchrony between the two coupled neurons. We then demonstrate a similar enhancement of synchrony in the MCI with dynamic synaptic modulation. For the MCI we also consider heterogeneity introduced in the network through the synaptic parameters: the synaptic decay time of mutual inhibition and the self inhibition synaptic strength. We show that the MCI exhibits enhanced synchrony in the presence of all the above mentioned sources of heterogeneity and the mechanism for this enhanced synchrony is similar to the case of the UCI.}, number={2}, journal={Journal of Computational Neuroscience}, author={Talathi, S.S. and Hwang, D.-U. and Ditto, W.L.}, year={2008}, pages={262–281} }
 @article{talathi_abarbanel_ditto_2008, title={Temporal spike pattern learning}, volume={78}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-53449087688&partnerID=MN8TOARS}, DOI={10.1103/PhysRevE.78.031918}, abstractNote={Sensory systems pass information about an animal's environment to higher nervous system units through sequences of action potentials. When these action potentials have essentially equivalent wave forms, all information is contained in the interspike intervals (ISIs) of the spike sequence. How do neural circuits recognize and read these ISI sequences? We address this issue of temporal sequence learning by a neuronal system utilizing spike timing dependent plasticity (STDP). We present a general architecture of neural circuitry that can perform the task of ISI recognition. The essential ingredients of this neural circuit, which we refer to as "interspike interval recognition unit" (IRU) are (i) a spike selection unit, the function of which is to selectively distribute input spikes to downstream IRU circuitry; (ii) a time-delay unit that can be tuned by STDP; and (iii) a detection unit, which is the output of the IRU and a spike from which indicates successful ISI recognition by the IRU. We present two distinct configurations for the time-delay circuit within the IRU using excitatory and inhibitory synapses, respectively, to produce a delayed output spike at time t_{0}+tau(R) in response to the input spike received at time t_{0} . R is the tunable parameter of the time-delay circuit that controls the timing of the delayed output spike. We discuss the forms of STDP rules for excitatory and inhibitory synapses, respectively, that allow for modulation of R for the IRU to perform its task of ISI recognition. We then present two specific implementations for the IRU circuitry, derived from the general architecture that can both learn the ISIs of a training sequence and then recognize the same ISI sequence when it is presented on subsequent occasions.}, number={3}, journal={Physical Review E - Statistical, Nonlinear, and Soft Matter Physics}, author={Talathi, S.S. and Abarbanel, H.D.I. and Ditto, W.L.}, year={2008} }
 @article{simonotto_furman_ditto_miliotis_spano_beaver_2007, title={Dynamic transmurality: Cardiac optical mapping reveals waves travel across transmural ablation lines}, volume={17}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-36749023290&partnerID=MN8TOARS}, DOI={10.1142/S0218127407018981}, abstractNote={Cardiac ablation is increasingly used to interdict the complex propagation of excitatory waves during atrial fibrillation. While such procedures are useful, they can often fail. Here we use fluorescence imaging to observe the electrical activity of an ablated porcine heart. We find that, while ablation lines do attenuate cardiac waves, the attenuation is incomplete. A remnant of the incident wave survives passage through the ablation barrier, albeit as a subthreshold signal. More importantly, we have found that these subthreshold signals may add constructively and thereby dynamically reduce the effective attenuation, an effect which we call "dynamic transmurality". We suspect this as a factor in the persistence of arrhythmia after ablative.}, number={9}, journal={International Journal of Bifurcation and Chaos}, author={Simonotto, J.D. and Furman, M.D. and Ditto, W.L. and Miliotis, A. and Spano, M.L. and Beaver, T.M.}, year={2007}, pages={3229–3234} }
 @inproceedings{talathi_hwang_ditto_carney_2007, title={Early seizure detection in an animal model of temporal lobe epilepsy}, volume={953}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-71449088557&partnerID=MN8TOARS}, DOI={10.1063/1.2817351}, abstractNote={The performance of five seizure detection schemes, i.e., Nonlinear embedding delay, Hurst scaling, Wavelet Scale, autocorrelation and gradient of accumulated energy, in their ability to detect EEG seizures close to the seizure onset time were evaluated to determine the feasibility of their application in the development of a real time closed loop seizure intervention program (RCLSIP). The criteria chosen for the performance evaluation were, high statistical robustness as determined through the predictability index, the sensitivity and the specificity of a given measure to detect an EEG seizure, the lag in seizure detection with respect to the EEG seizure onset time, as determined through visual inspection and the computational efficiency for each detection measure. An optimality function was designed to evaluate the overall performance of each measure dependent on the criteria chosen. While each of the above measures analyzed for seizure detection performed very well in terms of the statistical parameters, the nonlinear embedding delay measure was found to have the highest optimality index due to its ability to detect seizure very close to the EEG seizure onset time, thereby making it the most suitable dynamical measure in the development of RCLSIP in rat model with chronic limbic epilepsy.}, booktitle={AIP Conference Proceedings}, author={Talathi, S.S. and Hwang, D.-U. and Ditto, W. and Carney, P.R.}, year={2007}, pages={292–307} }
 @article{jahed-motlagh_kia_ditto_sinha_2007, title={Fault tolerance and detection in chaotic computers}, volume={17}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-34548434849&partnerID=MN8TOARS}, DOI={10.1142/S0218127407018142}, abstractNote={We introduce a structural testing method for a dynamics based computing device. Our scheme detects different physical defects, manifesting themselves as parameter variations in the chaotic system at the core of the logic blocks. Since this testing method exploits the dynamical properties of chaotic systems to detect damaged logic blocks, the damaged elements can be detected by very few testing inputs, leading to very low testing time. Further the method does not entail dedicated or extra hardware for testing. Specifically, we demonstrate the method on one-dimensional unimodal chaotic maps. Some ideas for testing higher dimensional maps and flows are also presented.}, number={6}, journal={International Journal of Bifurcation and Chaos}, author={Jahed-Motlagh, M.R. and Kia, B. and Ditto, W.L. and Sinha, S.}, year={2007}, pages={1955–1968} }
 @article{wessel_kurths_ditto_bauernschmitt_2007, title={Introduction: Cardiovascular physics}, volume={17}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-34047163882&partnerID=MN8TOARS}, DOI={10.1063/1.2718395}, abstractNote={The number of patients suffering from cardiovascular diseases increases unproportionally high with the increase of the human population and aging, leading to very high expenses in the public health system. Therefore, the challenge of cardiovascular physics is to develop high-sophisticated methods which are able to, on the one hand, supplement and replace expensive medical devices and, on the other hand, improve the medical diagnostics with decreasing the patient's risk. Cardiovascular physics-which interconnects medicine, physics, biology, engineering, and mathematics-is based on interdisciplinary collaboration of specialists from the above scientific fields and attempts to gain deeper insights into pathophysiology and treatment options. This paper summarizes advances in cardiovascular physics with emphasis on a workshop held in Bad Honnef, Germany, in May 2005. The meeting attracted an interdisciplinary audience and led to a number of papers covering the main research fields of cardiovascular physics, including data analysis, modeling, and medical application. The variety of problems addressed by this issue underlines the complexity of the cardiovascular system. It could be demonstrated in this Focus Issue, that data analyses and modeling methods from cardiovascular physics have the ability to lead to significant improvements in different medical fields. Consequently, this Focus Issue of Chaos is a status report that may invite all interested readers to join the community and find competent discussion and cooperation partners.}, number={1}, journal={Chaos}, author={Wessel, N. and Kurths, J. and Ditto, W. and Bauernschmitt, R.}, year={2007} }
 @inproceedings{simonotto_myers_furman_norman_liu_demarse_carney_ditto_2006, title={Coherence analysis over the latent period of epileptogenesis reveal that high-frequency communication is increased across hemispheres in an animal model of limbic epilepsy}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-34047097445&partnerID=MN8TOARS}, DOI={10.1109/IEMBS.2006.259817}, abstractNote={A total of 32 microwire electrodes were implanted bilaterally into the hippocampus of Sprague-Dawley rats, which were then stimulated in the manner prescribed for the chronic limbic epilepsy model. After the initial seizure brought on by the stimulation, the animals were recorded at a high sampling rate (approximately 12 kHz) for the entire duration of the latent period. Coherence was calculated across channels in both stimulated (and later seizing) animals and non-stimulated (and thus non-seizing control) animals. Average coherence over time was greatest in intrahemispherical electrode pairs in both stimulated and non-stimulated animals. However, the 200-800 Hz band displays increased coherence interhemispherically and up to 200 Hz band displays decreased coherence interhemispherically: this occurs only in stimulated animals.}, booktitle={Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings}, author={Simonotto, J.D. and Myers, S.M. and Furman, M.D. and Norman, W.M. and Liu, Z. and Demarse, T.B. and Carney, P.R. and Ditto, W.L.}, year={2006}, pages={1154–1156} }
 @article{simonotto_myers_furman_norman_liu_demarse_carney_ditto_2006, title={Coherence analysis over the latent period of epileptogenesis reveal that high-frequency communication is increased across hemispheres in an animal model of limbic epilepsy.}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84903876821&partnerID=MN8TOARS}, journal={Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Conference}, author={Simonotto, J.D. and Myers, S.M. and Furman, M.D. and Norman, W.M. and Liu, Z. and DeMarse, T.B. and Carney, P.R. and Ditto, W.L.}, year={2006}, pages={1154–1156} }
 @article{nelson_myers_simonotto_furman_spano_norman_liu_demarse_carney_ditto_2006, title={Detection of high frequency oscillations with Teager energy in an animal model of limbic epilepsy.}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84903856887&partnerID=MN8TOARS}, journal={Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Conference}, author={Nelson, R. and Myers, S.M. and Simonotto, J.D. and Furman, M.D. and Spano, M. and Norman, W.M. and Liu, Z. and DeMarse, T.B. and Carney, P.R. and Ditto, W.L.}, year={2006}, pages={2578–2580} }
 @inproceedings{nelson_myers_simonotto_furman_spano_norman_zhao_demarse_carney_ditto_2006, title={Detection of high frequency oscillations with teager energy in an animal model of limbic epilepsy}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-34047149543&partnerID=MN8TOARS}, DOI={10.1109/IEMBS.2006.259694}, abstractNote={High frequency oscillations (HFO) in limbic epilepsy represent a marked difference between abnormal and normal brain activity. Faced with the difficult of visually detecting HFOs in large amounts of intracranial EEG data, it is necessary to develop an automated process. This paper presents Teager Energy as a method of finding HFOs. Teager energy is an ideal measure because unlike conventional energy it takes into account the frequency component of the signal as well as signal amplitude. This greatly aids in the dissection of HFOs out of the noise and other signals contained in the EEG. Therein, Teager energy analysis is able to detect high-frequency, low-amplitude components that conventional energy measurements would miss}, booktitle={Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings}, author={Nelson, R. and Myers, S.M. and Simonotto, J.D. and Furman, M.D. and Spano, M. and Norman, W.M. and Zhao, L. and DeMarse, T.B. and Carney, P.R. and Ditto, W.L.}, year={2006}, pages={2578–2580} }
 @article{sanchez_mareci_norman_principe_ditto_carney_2006, title={Evolving into epilepsy: Multiscale electrophysiological analysis and imaging in an animal model}, volume={198}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-32644443817&partnerID=MN8TOARS}, DOI={10.1016/j.expneurol.2005.10.031}, abstractNote={Epilepsy research for the design of seizure detection/prediction neuroprosthetics has been faced with the search for electrophysiologic control parameters that can be used to infer the epileptic state of the animal and be leveraged at a later time to deliver neurotherapeutic feedback. The analysis presented here uses multi-microelectrode array technology to provide an electrophysiologic quantification of a hippocampal neural ensemble during the latent period of epileptogenesis. Through the use of signal processing system identification methodologies, we were able to assess the spatial and temporal interrelations of ensembles of hippocampal neurons and relate them to the evolution of the epileptic condition. High-field magnetic resonance (MR) imaging was used to determine the location of electrode placement and to evaluate hippocampal pyramidal cell structural damage. Long-term single unit activity analysis suggests that hippocampal neurons in both CA1-2 and dentate regions increase the number of occurrences and duration of their bursting activity after injury to the contra-lateral hippocampus. The trends inferred from both single neuron and ensemble analysis suggests that the evolution into epilepsy is not abrupt but modulates gradually from the time of injury.}, number={1}, journal={Experimental Neurology}, author={Sanchez, J.C. and Mareci, T.H. and Norman, W.M. and Principe, J.C. and Ditto, W.L. and Carney, P.R.}, year={2006}, pages={31–47} }
 @inproceedings{ditto_mural_sinha_2006, title={Exploiting chaos for computation}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-50249147740&partnerID=MN8TOARS}, DOI={10.1109/APCCAS.2006.342195}, abstractNote={We review the concept of the chaos computing paradigm, which exploits the controlled richness of nonlinear dynamics to obtain flexible reconfigurable hardware. We demonstrate the idea with specific schemes and verify the schemes through proof-of-principle experiments. Further we indicate the latest technological advances in the field.}, booktitle={IEEE Asia-Pacific Conference on Circuits and Systems, Proceedings, APCCAS}, author={Ditto, W.L. and Mural, K. and Sinha, S.}, year={2006}, pages={1835–1838} }
 @inproceedings{miliotis_ditto_sinha_2006, title={Exploiting nonlinear dynamics to search for the existence of matches in a database}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-50249125869&partnerID=MN8TOARS}, DOI={10.1109/APCCAS.2006.342197}, abstractNote={We propose a method that uses nonlinear dynamics to address the task of determining the existence of a specific item in an unsorted arbitrarily large database. The scheme involves a single global operation applied simultaneously to all elements of the database and a single global monitoring threshold for verification of existence. We also show how this global threshold can be altered for identification of the existence of items with characteristics close to the searched one}, booktitle={IEEE Asia-Pacific Conference on Circuits and Systems, Proceedings, APCCAS}, author={Miliotis, A. and Ditto, W.L. and Sinha, S.}, year={2006}, pages={1843–1846} }
 @article{sinha_ditto_2006, title={Exploiting the controlled responses of chaotic elements to design configurable hardware}, volume={364}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-33748313113&partnerID=MN8TOARS}, DOI={10.1098/rsta.2006.1836}, abstractNote={We discuss how threshold mechanisms can be effectively employed to control chaotic systems onto stable fixed points and limit cycles of widely varying periodicities. Then, we outline the theory and experimental realization of fundamental logic-gates from a chaotic system, using thresholding to effect control. A key feature of this implementation is that a single chaotic 'processor' can be flexibly configured (and re-configured) to emulate different fixed or dynamic logic gates through the simple manipulation of a threshold level.}, number={1846}, journal={Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences}, author={Sinha, S. and Ditto, W.L.}, year={2006}, pages={2483–2494} }
 @inproceedings{mishra_jones_simonotto_furman_norman_zhao_demarse_carney_ditto_2006, title={Pre-ictal entropy analysis of microwire data from an animal model of limbic epilepsy}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-34047174896&partnerID=MN8TOARS}, DOI={10.1109/IEMBS.2006.259685}, abstractNote={Epilepsy is a common neurological disorder that can have damaging effects in the brain including over 50% loss of neuronal activity in the hippocampal regions of the CA1 and CA3. The pre-ictal period was studied in an animal model of limbic epilepsy using Shannon entropy and correlation analysis. The primary aim was to uncover underlying relative changes in signals between the Dentate Gyrus and CA1 areas of the bilateral hippocampus. Preliminary entropy analysis results included dynamical changes between channels in the Dentate Gyrus and channels in the CA1 region at and around the time of the seizure.}, booktitle={Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings}, author={Mishra, M. and Jones, B. and Simonotto, J.D. and Furman, M.D. and Norman, W.M. and Zhao, L. and DeMarse, T.B. and Carney, P.R. and Ditto, W.L.}, year={2006}, pages={1605–1607} }
 @article{mishra_jones_simonotto_furman_norman_liu_demarse_carney_ditto_2006, title={Pre-ictal entropy analysis of microwire data from an animal model of limbic epilepsy.}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84903863001&partnerID=MN8TOARS}, journal={Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Conference}, author={Mishra, M. and Jones, B. and Simonotto, J.D. and Furman, M.D. and Norman, W.M. and Liu, Z. and DeMarse, T.B. and Carney, P.R. and Ditto, W.L.}, year={2006}, pages={1605–1607} }
 @inproceedings{murali_sinha_ditto_2006, title={Reconfigurable logic element using a chaotic circuit}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-50249118167&partnerID=MN8TOARS}, DOI={10.1109/APCCAS.2006.342196}, abstractNote={We report the experimental realization of all the fundamental logic gates, flexibly, using a chaotic circuit. In our scheme a simple threshold mechanism allows the chaotic circuit unit to switch easily between behaviours emulating the different gates. We also demonstrate the ability of on-the-fly dynamic reconfiguration of this logic cell.}, booktitle={IEEE Asia-Pacific Conference on Circuits and Systems, Proceedings, APCCAS}, author={Murali, K. and Sinha, S. and Ditto, W.L.}, year={2006}, pages={1839–1842} }
 @article{furman_simonotto_beaver_spano_ditto_2006, title={Using recurrence quantification analysis determinism for noise removal in cardiac optical mapping}, volume={53}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-33645298207&partnerID=MN8TOARS}, DOI={10.1109/TBME.2006.870195}, abstractNote={Selecting signal processing parameters in optical imaging by utilizing the change in Determinism, a measure introduced in Recurrence Quantification Analysis, provides a novel method using the change in residual noise Determinism for improving noise quantification and removal across signals exhibiting disparate underlying tissue pathologies. The method illustrates an improved process for selecting filtering parameters and how using measured signal-to-noise ratio alone can lead to improper parameter selection.}, number={4}, journal={IEEE Transactions on Biomedical Engineering}, author={Furman, M.D. and Simonotto, J.D. and Beaver, T.M. and Spano, M.L. and Ditto, W.L.}, year={2006}, pages={767–770} }
 @article{murali_sinha_ditto_2005, title={Construction of a reconfigurable dynamic logic cell}, volume={64}, ISSN={0304-4289 0973-7111}, url={http://dx.doi.org/10.1007/BF02704569}, DOI={10.1007/BF02704569}, number={3}, journal={Pramana}, publisher={Springer Science and Business Media LLC}, author={Murali, K. and Sinha, Sudeshna and Ditto, William L.}, year={2005}, month={Mar}, pages={433–441} }
 @inproceedings{simonotto_furman_ditto_spano_liu_kavanagh_2005, title={Nonlinear analysis of cardiac optical mapping data reveals ordered period in defibrillation failure}, volume={32}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-33847124926&partnerID=MN8TOARS}, DOI={10.1109/CIC.2005.1588160}, abstractNote={A high-speed video camera and voltage-sensitive dyes were used to acquire high resolution (80times80 pixels) and high-speed (500mus/frame) optical signals of ventricular fibrillation in a Langendorff-perfused porcine heart. The resulting spatiotemporal dynamics were recorded before and after the application of a defibrillation shock in order to study the mechanism of defibrillation failure. We used recurrence plots as a tool to qualify the evolution of ordered behavior on the heart surface before fibrillation was reestablished in defibrillation failure. Such ordered periods may point to robust periods in which the defibrillation attempt has had the most effect and may provide a window in which a smaller, corrective shock may be applied to achieve defibrillation}, booktitle={Computers in Cardiology}, author={Simonotto, J.D. and Furman, M.D. and Ditto, W.L. and Spano, M.L. and Liu, G. and Kavanagh, K.M.}, year={2005}, pages={551–554} }
 @inproceedings{ditto_2003, title={Chaos in Neural Systems: From Epilepsy to Neurocomputing}, volume={4}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-1542360051&partnerID=MN8TOARS}, booktitle={Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings}, author={Ditto, W.L.}, year={2003}, pages={3830–3833} }
 @article{murali_sinha_ditto_2003, title={Implementation of NOR gate by a chaotic Chua's circuit}, volume={13}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0242508464&partnerID=MN8TOARS}, DOI={10.1142/S0218127403008053}, abstractNote={We report the experimental implementation of the most fundamental NOR gate with a chaotic Chua's circuit by a simple threshold mechanism. This provides a proof-of-principle experiment to demonstrate the universal computing capability of chaotic circuits in continuous time systems.}, number={9}, journal={International Journal of Bifurcation and Chaos in Applied Sciences and Engineering}, author={Murali, K. and Sinha, S. and Ditto, W.L.}, year={2003}, pages={2669–2672} }
 @inproceedings{simonotto_furman_ditto_spano_liu_kavanagh_2003, title={Nonlinear Analysis of Failed Ventricular Defibrillation}, volume={1}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-1542362570&partnerID=MN8TOARS}, booktitle={Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings}, author={Simonotto, J.D. and Furman, M.D. and Ditto, W.L. and Spano, M.L. and Liu, G. and Kavanagh, K.M.}, year={2003}, pages={196–199} }
 @article{murali_sinha_ditto_2003, title={Realization of the fundamental NOR gate using a chaotic circuit}, volume={68}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-17144383290&partnerID=MN8TOARS}, number={1 2}, journal={Physical Review E - Statistical, Nonlinear, and Soft Matter Physics}, author={Murali, K. and Sinha, S. and Ditto, W.L.}, year={2003}, pages={162051–162055} }
 @inbook{spano_ditto_dolan_moss_2003, title={Unstable Periodic Orbits (UPOs) and Chaos Control in Neural Systems}, ISBN={9783642076657 9783662050484}, url={http://dx.doi.org/10.1007/978-3-662-05048-4_17}, DOI={10.1007/978-3-662-05048-4_17}, booktitle={Epilepsy as a Dynamic Disease}, publisher={Springer Berlin Heidelberg}, author={Spano, M. L. and Ditto, W. L. and Dolan, K. and Moss, F.}, year={2003}, pages={297–322} }
 @inproceedings{furman_simonotto_beaver_spano_ditto_liu_kavanagh_2003, title={Voltage-sensitive optical mapping for atrial fibrillation ablation treatment}, volume={1}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-1542332789&partnerID=MN8TOARS}, booktitle={Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings}, author={Furman, M.D. and Simonotto, J.D. and Beaver, T.M. and Spano, M.L. and Ditto, W.L. and Liu, G. and Kavanagh, K.M.}, year={2003}, pages={145–147} }
 @article{munakata_sinha_ditto_2002, title={Chaos computing: Implementation of fundamental logical gates by chaotic elements}, volume={49}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0036857050&partnerID=MN8TOARS}, DOI={10.1109/TCSI.2002.804551}, abstractNote={Basic principles of implementing the most fundamental computing functions by chaotic elements are described. They provide a theoretical foundation of computer architecture based on a totally new principle other than silicon chips. The fundamental functions are: the logical AND, OR, NOT, XOR, and NAND operations (gates) and bit-by-bit arithmetic operations. Each of the logical operations is realized by employing a single chaotic element. Computer memory can be constructed by combining logical gates. With these fundamental ingredients in hand, it is conceivable to build a simple, fast, yet cost effective, general-purpose computing device. Chaos computing may also lead to dynamic architecture, where the hardware design itself evolves during the course of computation.. The basic ideas are explained by employing a one-dimensional model, specifically the logistic map.}, number={11}, journal={IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications}, author={Munakata, T. and Sinha, S. and Ditto, W.L.}, year={2002}, pages={1629–1633} }
 @article{sinha_munakata_ditto_2002, title={Flexible parallel implementation of logic gates using chaotic elements}, volume={65}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-37649030639&partnerID=MN8TOARS}, DOI={10.1103/PhysRevE.65.036216}, abstractNote={We demonstrate the basic principles for the direct and flexible implementation of all basic logical operations utilizing low dimensional chaos. Then we generalize the concept to high dimensional chaotic systems, and show the parallelism inherent in such systems. As a case study we implement the proposed parallel computing architecture to obtain parallelized bit-by-bit addition with a two-dimensional chaotic neuronal and a three-dimensional chaotic laser model.}, number={3}, journal={Physical Review E - Statistical, Nonlinear, and Soft Matter Physics}, author={Sinha, S. and Munakata, T. and Ditto, W.L.}, year={2002} }
 @misc{ditto_2002, title={Keeping in sync}, volume={415}, DOI={10.1038/415736b}, number={6873}, journal={Nature}, author={Ditto, William L.}, year={2002}, month={Feb}, pages={736–737} }
 @article{meadows_heath_neff_brown_fogliatti_gabbay_in_hasler_deweerth_ditto_2002, title={Nonlinear antenna technology}, volume={90}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-33646891329&partnerID=MN8TOARS}, DOI={10.1109/JPROC.2002.1015012}, abstractNote={Nonlinear antennas combine advances in nonlinear dynamics, active antenna design, and analog microelectronics to generate beam steering and beam forming across an array of nonlinear oscillators. Nonlinear antennas exploit two phenomena typically shunned in traditional designs: nonlinear unit cells and interelement coupling. The design stems from nonlinear coupled differential equation analysis that by virtue of the dynamic control is far less complex than the linear counterparts by eliminating the need for phase shifters and beam forming computers. These advantages arise from incorporating nonlinear dynamics rather than limiting the system to linear quasisteady state operation. A theoretical framework describing beam shaping and beam forming by exploiting the phase, amplitude, and coupling dynamics of nonlinear oscillator arrays is presented. Experimental demonstration of nonlinear beam steering is realized using analog microelectronics.}, number={5}, journal={Proceedings of the IEEE}, author={Meadows, B.K. and Heath, T.H. and Neff, J.D. and Brown, E.A. and Fogliatti, D.W. and Gabbay, M. and In, V. and Hasler, P. and Deweerth, S.P. and Ditto, W.L.}, year={2002}, pages={882–896} }
 @article{sinha_munakata_ditto_2002, title={Parallel computing with extended dynamical systems}, volume={65}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-37649027841&partnerID=MN8TOARS}, DOI={10.1103/PhysRevE.65.036214}, abstractNote={We discuss the scope of parallelism based on extended dynamical systems, in particular, arrays of chaotic elements. As a case study we demonstrate the rapid solution of the Deutsch-Jozsa problem, utilizing the collective properties of such systems.}, number={3}, journal={Physical Review E - Statistical, Nonlinear, and Soft Matter Physics}, author={Sinha, S. and Munakata, T. and Ditto, W.L.}, year={2002} }
 @article{lindner_breen_bulsara_ditto_2002, title={Reply to “Comment on ‘Monostable array-enhanced stochastic resonance’ ”}, volume={66}, ISSN={1063-651X 1095-3787}, url={http://dx.doi.org/10.1103/physreve.66.013102}, DOI={10.1103/physreve.66.013102}, abstractNote={We take this opportunity to clarify issues raised in the preceding Comment by Soskin and McClintock [Phys. Rev. E. 66, 013101 (2002)]. In particular, we provide further details and results to motivate and explicate the methodologies we have employed to investigate stochastic resonance in arrays of monostable elements.}, number={1}, journal={Physical Review E}, publisher={American Physical Society (APS)}, author={Lindner, John F. and Breen, Barbara J. and Bulsara, Adi R. and Ditto, William L.}, year={2002}, month={Jul} }
 @inbook{ditto_2002, place={Boca Raton}, title={Spatio-temporal nonlinear dynamics: a new beginning}, ISBN={9780750308625 9781420033830}, DOI={10.1201/9781420033830.ch13}, booktitle={Nonlinear Dynamics and Chaos: Where do we go from here?}, publisher={CRC Press}, author={Ditto, William}, editor={Hogan, J. and Krauskopf, A.R. and di Bernado, Mario and Wilson, R. Eddie and Osinga, Hinke M. and Homer, Martin E. and Champneys, Alan R.Editors}, year={2002}, month={Aug} }
 @article{sinha_ditto_2001, title={Controlling neuronal spikes}, volume={63}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0035333398&partnerID=MN8TOARS}, number={5 II}, journal={Physical Review E - Statistical, Nonlinear, and Soft Matter Physics}, author={Sinha, S. and Ditto, W.L.}, year={2001}, pages={562091–562098} }
 @article{lindner_breen_wills_bulsara_ditto_2001, title={Monostable array-enhanced stochastic resonance}, volume={63}, ISSN={1063-651X 1095-3787}, url={http://dx.doi.org/10.1103/physreve.63.051107}, DOI={10.1103/physreve.63.051107}, abstractNote={We present a simple nonlinear system that exhibits multiple distinct stochastic resonances. By adjusting the noise and coupling of an array of underdamped, monostable oscillators, we modify the array's natural frequencies so that the spectral response of a typical oscillator in an array of N oscillators exhibits N-1 different stochastic resonances. Such families of resonances may elucidate and facilitate a variety of noise-mediated cooperative phenomena, such as noise-enhanced propagation, in a broad class of similar nonlinear systems.}, number={5}, journal={Physical Review E}, publisher={American Physical Society (APS)}, author={Lindner, John F. and Breen, Barbara J. and Wills, Meghan E. and Bulsara, Adi R. and Ditto, William L.}, year={2001}, month={Apr}, pages={511071–511076} }
 @article{lindner_mason_neff_breen_ditto_bulsara_2001, title={Noninvasive control of stochastic resonance}, volume={63}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0035304907&partnerID=MN8TOARS}, number={4 I}, journal={Physical Review E - Statistical, Nonlinear, and Soft Matter Physics}, author={Lindner, J.F. and Mason, J. and Neff, J. and Breen, B.J. and Ditto, W.L. and Bulsara, A.R.}, year={2001}, pages={411071–411078} }
 @article{ditto_2000, title={Chaos at 35,000 feet}, volume={3}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0033685795&partnerID=MN8TOARS}, DOI={10.1109/5289.846257}, abstractNote={The author discusses his experience in gaining investment and starting up a company to develop an improved defibrillation technique. He outlines his frustrations and daily hassles, and tells how an incident of airline passenger cardiac failure strengthened his resolve to continue. The company set up, Control Dynamics, although small, is functional. Over the last several years, many contracts have been won to develop chaos-control technology. Patent applications for chaos-based devices have been successful, and now we are intensely working toward practical applications of our research.}, number={2}, journal={IEEE Instrumentation and Measurement Magazine}, author={Ditto, W.L.}, year={2000}, pages={18–21} }
 @article{ditto_spano_in_neff_meadows_langberg_bolmann_mcteague_2000, title={Control of human atrial fibrillation}, volume={10}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0000156558&partnerID=MN8TOARS}, number={3}, journal={International Journal of Bifurcation and Chaos in Applied Sciences and Engineering}, author={Ditto, W.L. and Spano, M.L. and In, V. and Neff, J. and Meadows, B. and Langberg, J.J. and Bolmann, A. and McTeague, K.}, year={2000}, pages={593–601} }
 @inbook{ditto_spano_2000, place={Cambridge, UK}, title={Electromagnetic fields and biological tissues: from nonlinear response to chaos control}, ISBN={9780521624367 9780521026079 9780511535338}, url={http://dx.doi.org/10.1017/cbo9780511535338.021}, DOI={10.1017/cbo9780511535338.021}, booktitle={Self-Organized Biological Dynamics and Nonlinear Control}, publisher={Cambridge University Press}, author={Ditto, William L. and Spano, Mark L.}, editor={Walleczek, JanEditor}, year={2000}, month={May}, pages={341–373} }
 @article{löcher_chatterjee_marchesoni_ditto_hunt_2000, title={Noise sustained propagation: Local versus global noise}, volume={61}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0001368498&partnerID=MN8TOARS}, number={5 A}, journal={Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics}, author={Löcher, M. and Chatterjee, N. and Marchesoni, F. and Ditto, W.L. and Hunt, E.R.}, year={2000}, pages={4954–4961} }
 @article{mason_lindner_neff_ditto_bulsara_spano_2000, title={Pulse Enhanced Stochastic Resonance}, volume={277}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0034645014&partnerID=MN8TOARS}, DOI={10.1016/S0375-9601(00)00665-4}, abstractNote={Abstract By adding constant-amplitude pulses to a noisy bistable system, we enhance its response to monochromatic signals, significantly magnifying its unpulsed stochastic resonance. We observe the enhancement in both numerical simulations and in analog electronic experiments. This simple noninvasive control technique should be especially useful in noisy bistable systems that are difficult or impossible to modify internally.}, number={1}, journal={Physics Letters A}, author={Mason, Jonathan and Lindner, John F. and Neff, Joseph and Ditto, William L. and Bulsara, Adi and Spano, Mark}, year={2000}, pages={13–17} }
 @article{löcher_inchiosa_neff_bulsara_wiesenfeld_gammaitoni_hänggi_ditto_2000, title={Theory of controlling stochastic resonance}, volume={62}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0037726292&partnerID=MN8TOARS}, DOI={10.1103/PhysRevE.62.317}, abstractNote={The concept of controlling stochastic resonance has been recently introduced [L. Gammaitoni et al., Phys. Rev. Lett. 82, 4574 (1999)] to enhance or suppress the spectral response to threshold-crossing events triggered by a time-periodic signal in background noise. Here, we develop a general theoretical framework, based on a rate equation approach. This generic two-state theory captures the essential features observed in our experiments and numerical simulations.}, number={1 A}, journal={Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics}, author={Löcher, M. and Inchiosa, M.E. and Neff, J. and Bulsara, A. and Wiesenfeld, K. and Gammaitoni, L. and Hänggi, P. and Ditto, W.}, year={2000}, pages={317–327} }
 @inbook{spano_ditto_1999, place={New York}, title={Chaos Control in Biological Systems}, ISBN={9783527607457}, DOI={10.1002/3527607455.ch17}, abstractNote={This chapter contains sections titled: Introduction Cardiac Dynamics Introduction to ventricular fibrillation Fibrillation as a dynamical state Detection of deterministic dynamics in canine ventricular fibrillation Imaging of the spatiotemporal evolution of ventricular fibrillation Control of Chaos in Cardiac Systems Control of isolated cardiac tissue Control of atrial fibrillation in humans Control of Chaos in Brain Tissue DC Field Interactions with Mammalian Neuronal Tissue Summary}, booktitle={Handbook of Chaos Control}, publisher={Wiley-VCH}, author={Spano, Mark L. and Ditto, William L.}, editor={Schuster, H.G.Editor}, year={1999} }
 @article{ditto_1999, title={Chaos at 35,000 feet}, volume={5}, number={4}, journal={Industrial Physicist}, author={Ditto, William L.}, year={1999}, month={Aug}, pages={27–29} }
 @article{sinha_ditto_1999, title={Computing with distributed chaos}, volume={60}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-18144376447&partnerID=MN8TOARS}, number={1}, journal={Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics}, author={Sinha, S. and Ditto, W.L.}, year={1999}, pages={363–377} }
 @article{gammaitoni_löcher_bulsara_hänggi_neff_wiesenfeld_ditto_inchiosa_1999, title={Controlling stochastic resonance}, volume={82}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0000617726&partnerID=MN8TOARS}, number={23}, journal={Physical Review Letters}, author={Gammaitoni, L. and Löcher, M. and Bulsara, A. and Hänggi, P. and Neff, J. and Wiesenfeld, K. and Ditto, W. and Inchiosa, M.E.}, year={1999}, pages={4574–4577} }
 @article{witkowski_leon_penkoske_clark_spano_ditto_giles_1998, title={A method for visualization of ventricular fibrillation: Design of a cooled fiberoptically coupled image intensified CCD data acquisition system incorporating wavelet shrinkage based adaptive filtering}, volume={8}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0346207529&partnerID=MN8TOARS}, number={1}, journal={Chaos}, author={Witkowski, F.X. and Leon, L.J. and Penkoske, P.A. and Clark, R.B. and Spano, M.L. and Ditto, W.L. and Giles, W.R.}, year={1998}, pages={94–102} }
 @article{lindner_meadows_marsh_ditto_bulsara_1998, title={Can neurons distinguish chaos from noise?}, volume={8}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0040944349&partnerID=MN8TOARS}, number={4}, journal={International Journal of Bifurcation and Chaos in Applied Sciences and Engineering}, author={Lindner, J.F. and Meadows, B.K. and Marsh, T.L. and Ditto, W.L. and Bulsara, A.R.}, year={1998}, pages={767–781} }
 @article{sinha_ditto_1998, title={Dynamics based computation}, volume={81}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0001266470&partnerID=MN8TOARS}, number={10}, journal={Physical Review Letters}, author={Sinha, S. and Ditto, W.L.}, year={1998}, pages={2156–2159} }
 @article{lindner_chandramouli_bulsara_löcher_ditto_1998, title={Noise Enhance Propagation}, volume={81}, DOI={10.1103/PhysRevLett.81.5048}, abstractNote={We use noise to extend signal propagation in one- and two-dimensional arrays of two-way coupled bistable oscillators. In a numerical model, we sinusoidally force one end of a chain of noisy oscillators. We record a signal-to-noise ratio at each oscillator. We demonstrate that moderate noise significantly extends the propagation of the sinusoidal input. Oscillators far from the input, where noise extends the signal, exhibit a classical stochastic resonance. We obtain similar results with two-dimensional arrays. The simplicity of the model suggests the generality of the phenomenon.}, journal={Physical Review Letters}, author={Lindner, John F. and Chandramouli, Sridhar and Bulsara, Adi R. and Löcher, Markus and Ditto, William L.}, year={1998}, pages={5048} }
 @article{lindner_chandramouli_bulsara_löcher_ditto_1998, title={Noise enhanced propagation}, volume={81}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0001608554&partnerID=MN8TOARS}, number={23}, journal={Physical Review Letters}, author={Lindner, J.F. and Chandramouli, S. and Bulsara, A.R. and Löcher, M. and Ditto, W.L.}, year={1998}, pages={5048–5051} }
 @inproceedings{neff_patel_meadows_deweerth_ditto_1998, title={Spatiotemporal dynamics of a stochastic VLSI array}, volume={3}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0031624012&partnerID=MN8TOARS}, booktitle={Proceedings - IEEE International Symposium on Circuits and Systems}, author={Neff, Joseph D. and Patel, Girish N. and Meadows, Brian K. and DeWeerth, Stephen P. and Ditto, William L.}, year={1998}, pages={542–545} }
 @article{witkowski_leon_penkoske_giles_spano_ditto_winfree_1998, title={Spatiotemporal evolution of ventricular fibrillation}, volume={392}, number={6671}, journal={Nature}, publisher={Nature Publishing Group}, author={Witkowski, Francis X and Leon, L Joshua and Penkoske, Patricia A and Giles, Wayne R and Spano, Mark L and Ditto, William L and Winfree, Arthur T}, year={1998}, pages={78–82} }
 @article{ding_ding_ditto_gluckman_in_peng_spano_yang_1997, title={Control and synchronization of chaos in high dimensional systems: Review of some recent results}, volume={7}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0040453558&partnerID=MN8TOARS}, number={4}, journal={Chaos}, author={Ding, M. and Ding, E.-J. and Ditto, W.L. and Gluckman, B. and In, V. and Peng, J.-H. and Spano, M.L. and Yang, W.}, year={1997}, pages={644–652} }
 @article{ditto_showalter_1997, title={Introduction: Control and synchronization of chaos}, volume={7}, ISSN={1054-1500 1089-7682}, url={http://dx.doi.org/10.1063/1.166276}, DOI={10.1063/1.166276}, abstractNote={The hallmark of deterministic chaos, an extreme sensitivity to initial conditions, suggests that chaotic systems might be difficult if not impossible to control, since any perturbations used for control would grow exponentially in time. Indeed, this quite reasonable view was widely held until only a few years ago. Surprisingly, the basis for controlling chaos is provided by just this property, which allows carefully chosen, tiny perturbations to be used for stabilizing virtually any of the unstable periodic orbits making up a strange attractor. Ergodicity is another property of chaotic systems that makes them particularly amenable to control, since most points of interest are eventually visited in the natural evolution of the system. Other characteristics of nonlinear systems—together with the myriad tools of dynamical systems theory—allow the ‘‘dynamicist of the ’90s’’ to control complex behavior to an extent no one would have believed possible only a decade ago. In the papers in this Focus Issue, recent advances in methods for controlling dynamical systems along with applications of these methods in a wide range of experimental settings are described. Advances in the closely related topic of synchronization of chaotic systems are also featured. Research on controlling chaotic systems has seen remarkable growth in a short time span, with the ‘‘early’’ studies in the field appearing less than ten years ago. In the late}, number={4}, journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, publisher={AIP Publishing}, author={Ditto, William L. and Showalter, Kenneth}, year={1997}, month={Dec}, pages={509–511} }
 @inproceedings{spano_in_ditto_1997, title={Maintaining chaos}, volume={459}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0030643306&partnerID=MN8TOARS}, booktitle={Materials Research Society Symposium - Proceedings}, author={Spano, Mark L. and In, Visarath and Ditto, William L.}, year={1997}, pages={545–555} }
 @article{in_spano_neff_ditto_daw_edwards_nguyen_1997, title={Maintenance of chaos in a computational model of a thermal pulse combustor}, volume={7}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0011254491&partnerID=MN8TOARS}, number={4}, journal={Chaos}, author={In, V. and Spano, M.L. and Neff, J.D. and Ditto, W.L. and Daw, C.S. and Edwards, K.D. and Nguyen, K.}, year={1997}, pages={605–613} }
 @article{christini_in_spano_ditto_collins_1997, title={Real-time experimental control of a system in its chaotic and nonchaotic regimes}, volume={56}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0000616907&partnerID=MN8TOARS}, number={4}, journal={Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics}, author={Christini, D.J. and In, V. and Spano, M.L. and Ditto, W.L. and Collins, J.J.}, year={1997} }
 @article{gluckman_spano_yang_ding_in_ditto_1997, title={Tracking unstable periodic orbits in nonstationary high-dimensional chaotic systems: Method and experiment}, volume={55}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0001114969&partnerID=MN8TOARS}, number={5 A}, journal={Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics}, author={Gluckman, B.J. and Spano, M.L. and Yang, W. and Ding, M. and In, V. and Ditto, W.L.}, year={1997}, pages={4935–4942} }
 @article{ding_yang_in_ditto_spano_gluckman_1996, title={Controlling chaos in high dimensions: Theory and experiment}, volume={53}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0001158240&partnerID=MN8TOARS}, number={5 SUPPL. A}, journal={Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics}, author={Ding, M. and Yang, W. and In, V. and Ditto, W.L. and Spano, M.L. and Gluckman, B.}, year={1996}, pages={4334–4344} }
 @article{gluckman_neel_netoff_ditto_spano_schiff_1996, title={Electric field suppression of epileptiform activity in hippocampal slices}, volume={76}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0030473481&partnerID=MN8TOARS}, number={6}, journal={Journal of Neurophysiology}, author={Gluckman, B.J. and Neel, E.J. and Netoff, T.I. and Ditto, W.L. and Spano, M.L. and Schiff, S.J.}, year={1996}, pages={4202–4205} }
 @inproceedings{witkowski_penkoske_plonsey_kavanagh_giles_spano_ditto_1996, title={Novel mapping storage architecture enabling tens of thousands of channels on a personal computer platform}, volume={5}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0030316054&partnerID=MN8TOARS}, booktitle={Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings}, author={Witkowski, Francis X. and Penkoske, Patricia A. and Plonsey, Robert and Kavanagh, Katherine M. and Giles, Wayne R. and Spano, Mark L. and Ditto, William L.}, year={1996}, pages={1885–1886} }
 @article{lindner_meadows_ditto_inchiosa_bulsara_1996, title={Scaling laws for spatiotemporal synchronization and array enhanced stochastic resonance}, volume={53}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-4243891810&partnerID=MN8TOARS}, number={3}, journal={Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics}, author={Lindner, J.F. and Meadows, B.K. and Ditto, W.L. and Inchiosa, M.E. and Bulsara, A.R.}, year={1996}, pages={2081–2086} }
 @article{gluckman_netoff_neel_ditto_spano_schiff_1996, title={Stochastic resonance in a neuronal network from mammalian brain}, volume={77}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0000325573&partnerID=MN8TOARS}, number={19}, journal={Physical Review Letters}, author={Gluckman, B.J. and Netoff, T.I. and Neel, E.J. and Ditto, W.L. and Spano, M.L. and Schiff, S.J.}, year={1996}, pages={4098–4101} }
 @article{in_ditto_spano_1995, title={Adaptive control and tracking of chaos in a magnetoelastic ribbon}, volume={51}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0002270984&partnerID=MN8TOARS}, DOI={10.1103/PhysRevE.51.R2689}, abstractNote={We have implemented the tracking of unstable orbits using the full control method of Ott, Grebogi, and Yorke (OGY). (Previous implementations have used only limiting cases of the OGY method.) The implementation is achieved in a mechanical system, the magnetoelastic ribbon. In addition, a method is demonstrated whereby the OGY control parameter may be optimized using only experimental data.}, number={4}, journal={Physical Review E}, author={In, V. and Ditto, W.L. and Spano, M.L.}, year={1995} }
 @article{lindner_meadows_ditto_inchiosa_bulsara_1995, title={Array enhanced stochastic resonance and spatiotemporal synchronization}, volume={75}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-11944262392&partnerID=MN8TOARS}, DOI={10.1103/PhysRevLett.75.3}, abstractNote={We enhance the response of a ``stochastic resonator'' by coupling it into a chain of identical resonators. Specifically, we show via numerical simulation that local linear coupling of overdamped nonlinear oscillators significantly enhances the signal-to-noise ratio of the response of a single oscillator to a time-periodic signal and noise. We relate this array enhanced stochastic resonance to the global spatiotemporal dynamics of the array and show how noise, coupling, and bistable potential cooperate to organize spatial order, temporal periodicity, and peak signal-to-noise ratio.}, number={1}, journal={Physical Review Letters}, author={Lindner, J.F. and Meadows, B.K. and Ditto, W.L. and Inchiosa, M.E. and Bulsara, A.R.}, year={1995}, pages={3–6} }
 @article{garfinkel_weiss_ditto_spano_1995, title={Chaos control of cardiac arrhythmias}, volume={5}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0028902494&partnerID=MN8TOARS}, DOI={10.1016/1050-1738(94)00083-2}, abstractNote={Chaos theory has shown that many disordered and erratic phenomena are in fact deterministic, and can be understood causally and controlled. The prospect that cardiac arrhythmias might be instances of deterministic chaos is therefore intriguing. We used a recently developed method of chaos control to stabilize a ouabain-induced arrhythmia in rabbit ventricular tissue in vitro. Extension of these results to clinically significant arrhythmias such as fibrillation will require overcoming the additional obstacles of spatiotemporal complexity.}, number={2}, journal={Trends in Cardiovascular Medicine}, author={Garfinkel, A. and Weiss, J.N. and Ditto, W.L. and Spano, M.L.}, year={1995}, pages={76–80} }
 @inproceedings{witkowski_penkoske_plonsey_kaplan_spano_ditto_kavanagh_1995, title={Development of a nonlinearly deterministic signal generator for real time chaos control testing}, volume={17}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0029429376&partnerID=MN8TOARS}, number={1}, booktitle={Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings}, author={Witkowski, Francis X. and Penkoske, Patricia A. and Plonsey, Robert and Kaplan, Daniel T. and Spano, Mark L. and Ditto, William L. and Kavanagh, Katherine M.}, year={1995}, pages={287–288} }
 @article{braiman_ditto_wiesenfeld_spano_1995, title={Disorder-enhanced synchronization}, volume={206}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0001772946&partnerID=MN8TOARS}, DOI={10.1016/0375-9601(95)00570-S}, abstractNote={We find that an increase in the disorder of an array of Josephson junctions can lead to significant improvement in the synchronization of the array. Both this effect and the opposite, more expected behavior are seen over a broad parameter range.}, number={1-2}, journal={Physics Letters A}, author={Braiman, Y. and Ditto, W.L. and Wiesenfeld, K. and Spano, M.L.}, year={1995}, pages={54–60} }
 @article{nusse_yorke_ditto_1995, title={Dynamics: Numerical Explorations}, volume={48}, ISSN={0031-9228 1945-0699}, url={http://dx.doi.org/10.1063/1.2808104}, DOI={10.1063/1.2808104}, number={7}, journal={Physics Today}, publisher={AIP Publishing}, author={Nusse, Helena E. and Yorke, James A. and Ditto, William L.}, year={1995}, month={Jul}, pages={57–57} }
 @article{witkowski_kavanagh_penkoske_plonsey_spano_ditto_kaplan_1995, title={Evidence for determinism in ventricular fibrillation}, volume={75}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0001740162&partnerID=MN8TOARS}, DOI={10.1103/PhysRevLett.75.1230}, abstractNote={Using a recently formulated technique for in vivo cardiac transmembrane current estimation, we examined ventricular fibrillation for evidence of deterministic linear and nonlinear structure. Both unstable fixed point analysis and a newly formulated measure of nonlinear determinism indicated that ventricular fibrillation in vivo exhibits deterministic dynamics similar to those previously used in chaos control.}, number={6}, journal={Physical Review Letters}, author={Witkowski, F.X. and Kavanagh, K.M. and Penkoske, P.A. and Plonsey, R. and Spano, M.L. and Ditto, W.L. and Kaplan, D.T.}, year={1995}, pages={1230–1233} }
 @article{in_mahan_ditto_spano_1995, title={Experimental Maintenance of Chaos}, volume={74}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0000765353&partnerID=MN8TOARS}, DOI={10.1103/PhysRevLett.74.4420}, abstractNote={We present a method for the anticontrol or maintenance of chaos designed for easy application to physical and biological systems. The method is based on the return map of the experimental data and requires only small, very infrequently applied time-dependent perturbations of a single system parameter and does not require any model equations for or a priori knowledge of the system dynamics. The method is shown to be able to reliably sustain chaos in a magnetomechanical ribbon experiment.}, number={22}, journal={Physical Review Letters}, author={In, V. and Mahan, S.E. and Ditto, W.L. and Spano, M.L.}, year={1995}, pages={4420–4423} }
 @article{ditto_munakata_1995, title={Principles and applications of chaotic systems}, volume={38}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0029407991&partnerID=MN8TOARS}, DOI={10.1145/219717.219797}, abstractNote={There lies a behavior between rigid regularity and randomness based on pure chance. It's called a chaotic system, or chaos for short [5]. Chaos is all around us. Our notions of physical motion or dynamic systems have encompassed the precise clock-like ticking of periodic systems and the vagaries of dice-throwing chance, but have often been overlooked as a way to account for the more commonly observed chaotic behavior between these two extremes. When we see irregularity we cling to randomness and disorder for explanations. Why should this be so? Why is it that when the ubiquitous irregularity of engineering, physical, biological, and other systems are studied, it is assumed to be random and the whole vast machinery of probability and statistics is applied? Rather recently, however, we have begun to realize that the tools of chaos theory can be applied toward the understanding, manipulation, and control of a variety of systems, with many of the practical applications coming after 1990. To understand why this is true, one must start with a working knowledge of how chaotic systems behave—profoundly, but sometimes subtly different, from the behavior of random systems.}, number={11}, journal={Communications of the ACM}, author={Ditto, William and Munakata, Toshinori}, year={1995}, pages={96–102} }
 @article{lindner_ditto_1995, title={Removal, suppression, and control of chaos by nonlinear design}, volume={48}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0029515896&partnerID=MN8TOARS}, number={12 pt 1}, journal={Applied Mechanics Reviews}, author={Lindner, John F. and Ditto, William L.}, year={1995}, pages={795–808} }
 @article{braiman_lindner_ditto_1995, title={Taming spatiotemporal chaos with disorder}, volume={378}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0001747882&partnerID=MN8TOARS}, number={6556}, journal={Nature}, author={Braiman, Y. and Lindner, J.F. and Ditto, W.L.}, year={1995}, pages={465–467} }
 @article{ditto_spano_lindner_1995, title={Techniques for the control of chaos}, volume={86}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0000801336&partnerID=MN8TOARS}, DOI={10.1016/0167-2789(95)00101-9}, abstractNote={The concepts of chaos and its control are reviewed. Both are discussed from an experimental as well as a theoretical viewpoint. Examples are then given of the control of chaos in adiverse set of experimental systems. Current and future applications are discussed.}, number={1-2}, journal={Physica D: Nonlinear Phenomena}, author={Ditto, W.L. and Spano, M.L. and Lindner, J.F.}, year={1995}, pages={198–211} }
 @article{weiss_garfinkel_spano_ditto_1994, title={Chaos and chaos control in biology}, volume={93}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0028197657&partnerID=MN8TOARS}, number={4}, journal={Journal of Clinical Investigation}, author={Weiss, J.N. and Garfinkel, A. and Spano, M.L. and Ditto, W.L.}, year={1994}, pages={1355–1360} }
 @article{tsonis_ditto._1994, title={Chaos: From Theory to Applications}, volume={62}, ISSN={0002-9505 1943-2909}, url={http://dx.doi.org/10.1119/1.17594}, DOI={10.1119/1.17594}, abstractNote={First Page}, number={2}, journal={American Journal of Physics}, publisher={American Association of Physics Teachers (AAPT)}, author={Tsonis, Reviewed by Anastasios A. and Ditto., William L.}, year={1994}, month={Feb}, pages={190–191} }
 @article{schiff_jerger_duong_chang_spano_ditto_1994, title={Controlling chaos in the brain}, volume={370}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0028003827&partnerID=MN8TOARS}, DOI={10.1038/370615a0}, number={6491}, journal={Nature}, author={Schiff, S.J. and Jerger, K. and Duong, D.H. and Chang, T. and Spano, M.L. and Ditto, W.L.}, year={1994}, pages={615–620} }
 @article{witkowski_kavanagh_penkoske_plonsey_kaplan_spano_ditto_1994, title={In vivo transmembrane cardiac current determination provides evidence for unstable fixed points during ventricular fibrillation}, volume={10}, journal={Canadian Journal of Cardiology}, author={Witkowski, F. and Kavanagh, K. and Penkoske, P. and Plonsey, R. and Kaplan, D. and Spano, M. and Ditto, W.}, year={1994}, pages={94C} }
 @article{spano_ditto_1994, title={The fundamentals of controlling chaos}, volume={29}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0028478419&partnerID=MN8TOARS}, DOI={10.1007/BF02691328}, abstractNote={The concepts of chaos and its control are reviewed. Both are discussed from an experimental as well as a theoretical viewpoint. A detailed exposition of the mathematics of chaos control is presented, with an eye toward implementation in computer-controlled experiments.}, number={3}, journal={Integrative Physiological and Behavioral Science}, author={Spano, M.L. and Ditto, W.L.}, year={1994}, pages={235–245} }
 @article{ippen_lindner_ditto_1993, title={Chaotic resonance: A simulation}, volume={70}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-21144462434&partnerID=MN8TOARS}, DOI={10.1007/BF01053980}, number={1-2}, journal={Journal of Statistical Physics}, author={Ippen, E. and Lindner, J. and Ditto, W.L.}, year={1993}, pages={437–450} }
 @article{ditto_pecora_1993, title={Mastering Chaos}, volume={269}, ISSN={0036-8733}, url={http://dx.doi.org/10.1038/scientificamerican0893-78}, DOI={10.1038/scientificamerican0893-78}, number={2}, journal={Scientific American}, publisher={Springer Science and Business Media LLC}, author={Ditto, William L. and Pecora, Louis M.}, year={1993}, month={Aug}, pages={78–84} }
 @article{garfinkel_spano_ditto_weiss_1992, title={Controlling. cardiac chaos}, volume={257}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0026787809&partnerID=MN8TOARS}, number={5074}, journal={Science}, author={Garfinkel, A. and Spano, M.L. and Ditto, W.L. and Weiss, J.N.}, year={1992}, pages={1230–1235} }
 @article{spano_wun-fogle_ditto_1992, title={Experimental observation of stochastic resonance in a magnetoelastic ribbon}, volume={46}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-25344449991&partnerID=MN8TOARS}, DOI={10.1103/PhysRevA.46.5253}, abstractNote={We report the observation of stochastic resonance in a parametrically driven bistable magnetoelastic buckling-ribbon experiment. We have found that the parametric addition of white noise increases the signal-to-noise ratio of the response of the ribbon by 10 to 12 dB relative to that of the ribbon with no externally added noise. We have also observed a characteristic spectrum for the probability of residence times for this weakly bistable system.}, number={8}, journal={Physical Review A}, author={Spano, M.L. and Wun-Fogle, M. and Ditto, W.L.}, year={1992}, pages={5253–5256} }
 @article{shinbrot_ditto_grebogi_ott_spano_yorke_1992, title={Using the sensitive dependence of chaos (the eebutterfly effectee) to direct trajectories in an experimental chaotic system}, volume={68}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0000301863&partnerID=MN8TOARS}, DOI={10.1103/PhysRevLett.68.2863}, abstractNote={In this paper we present the first experimental verification that the sensitivity of a chaotic system to small perturbations (the ``butterfly effect'') can be used to rapidly direct orbits from an arbitrary initial state to an arbitrary accessible desired state.}, number={19}, journal={Physical Review Letters}, publisher={APS}, author={Shinbrot, T. and Ditto, W. and Grebogi, C. and Ott, E. and Spano, M. and Yorke, J.A.}, year={1992}, pages={2863–2866} }
 @article{heagy_ditto_1991, title={Dynamics of a two-frequency parametrically driven duffing oscillator}, volume={1}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0001631940&partnerID=MN8TOARS}, DOI={10.1007/BF02429848}, number={4}, journal={Journal of Nonlinear Science}, author={Heagy, J. and Ditto, W.L.}, year={1991}, pages={423–455} }
 @article{sommerer_ditto_grebogi_ott_spano_1991, title={Experimental confirmation of the scaling theory for noise-induced crises}, volume={66}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0000164168&partnerID=MN8TOARS}, DOI={10.1103/PhysRevLett.66.1947}, abstractNote={We investigate experimentally the scaling of the average time \ensuremath{\tau} between intermittent, noise-induced bursts for a chaotic mechanical system near a crisis. The system studied is a periodically driven (frequency f) magnetoelastic ribbon. Theory predicts that for deterministic crises where \ensuremath{\tau} scales as \ensuremath{\tau}\ensuremath{\sim}\ensuremath{\Vert}f-${\mathit{f}}_{\mathit{c}}$${\mathrm{\ensuremath{\Vert}}}^{\mathrm{\ensuremath{-}}\ensuremath{\gamma}}$ (f${\mathit{f}}_{\mathit{c}}$, f=${\mathit{f}}_{\mathit{c}}$ at crisis), the characteristic time between noise-induced bursts (f\ensuremath{\ge}${\mathit{f}}_{\mathit{c}}$) should scale as \ensuremath{\tau}\ensuremath{\sim}${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}\ensuremath{\gamma}}$g(\ensuremath{\Vert}f-${\mathit{f}}_{\mathit{c}}$\ensuremath{\Vert}/\ensuremath{\sigma}), where \ensuremath{\sigma} is the noise strength and \ensuremath{\gamma} is the same in both cases. We determine \ensuremath{\gamma} for the low-noise (``deterministic'') system, then add noise and observe that the scaling for \ensuremath{\tau} is as predicted.}, number={15}, journal={Physical Review Letters}, author={Sommerer, J.C. and Ditto, W.L. and Grebogi, C. and Ott, E. and Spano, M.L.}, year={1991}, pages={1947–1950} }
 @article{sommerer_ditto_grebogi_ott_spano_1991, title={Experimental confirmation of the theory for critical exponents of crisis}, volume={153}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-6144267833&partnerID=MN8TOARS}, DOI={10.1016/0375-9601(91)90848-3}, abstractNote={Abstract We investigate the scaling of the average time τ between intermittent bursts for a chaotic system that undergoes a homoclinic tangency crisis, which causes a sudden expansion in the attractor. The system studied is a periodically driven (frequency f), nonlinear, magnetoelastic ribbon. The observed behavior of τ is well fit by a power-law scaling τ ∼| f − f c | − γ , where f = f c at the crisis. We identify the unstable periodic orbit mediating the crisis, and detemine its linearized eigenvalues from experimental data. The critical exponent γ found from the scaling of τ is shown to agree with that theoretically predicted for a two-dimensional map on the basis of the eigenvalues of the mediating periodic orbit.}, number={2-3}, journal={Physics Letters A}, author={Sommerer, J.C. and Ditto, W.L. and Grebogi, C. and Ott, E. and Spano, M.L.}, year={1991}, pages={105–109} }
 @article{spano_ditto_rauseo_1991, title={Exploitation of chaos for active control: an experiment}, volume={2}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0026240343&partnerID=MN8TOARS}, number={4}, journal={Journal of Intelligent Material Systems and Structures}, author={Spano, M.L. and Ditto, W.L. and Rauseo, S.N.}, year={1991}, pages={482–493} }
 @article{crisis-induced intermittency in a parametrically driven, gravitationally buckled, magnetoelastic amorphous ribbon experiment (invited)_1990, volume={67}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-5244307626&partnerID=MN8TOARS}, DOI={10.1063/1.345905}, abstractNote={Transversely annealed amorphous metallic glass ribbons exhibit extremely large magnetoelastic coupling. Consequently, the Young’s modulus of this material can be altered by a factor of 10 with the application of a small magnetic field. This effect is exploited to drive a vertically aligned ribbon, clamped at the bottom and free at the end, by buckling the ribbon gravitationally. Periodic, quasiperiodic, intermittent, and chaotic behavior are observed experimentally. A model for the system is also presented.}, number={9}, journal={Journal of Applied Physics}, year={1990}, pages={5619–5623} }
 @article{ditto_spano_savage_rauseo_heagy_ott_1990, title={Erratum: Experimental observation of a stranger nonchaotic attractor (Physical Review Letters (1990) 65, 9 (1172))}, volume={65}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-35949008548&partnerID=MN8TOARS}, DOI={10.1103/PhysRevLett.65.1172.2}, number={9}, journal={Physical Review Letters}, author={Ditto, W.L. and Spano, M.L. and Savage, H.T. and Rauseo, S.N. and Heagy, J. and Ott, E.}, year={1990} }
 @article{ditto_pickett_1990, title={Exact solutions of nonlinear differential equations using continued fractions}, volume={105}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-51649156991&partnerID=MN8TOARS}, DOI={10.1007/BF02728824}, abstractNote={The continued-fraction conversion method (J. Math. Phys. (N. Y.),29, 1761 (1988)) is used to generate a homologous family of exact solutions to the Lane-Emden equation ϕ(r)″+2ϕ(r)′/r+αϕ(r) p =0, forp=5. An exact solution is also obtained for a generalization of the Lane-Emden equation of the form −ϕ(r)″−2ϕ(r)′/r+αϕ(r)2p+1+λϕ(r)4p+1=0 for arbitrary α, γ andp. A condition is established for the generation of exact solutions from the method.}, number={4}, journal={Il Nuovo Cimento B Series 11}, author={Ditto, W.L. and Pickett, T.J.}, year={1990}, pages={429–435} }
 @article{ditto_rauseo_spano_1990, title={Experimental control of chaos}, volume={65}, ISSN={0031-9007}, url={http://dx.doi.org/10.1103/physrevlett.65.3211}, DOI={10.1103/PhysRevLett.65.3211}, abstractNote={It was demonstrated that one can convert the motion of a chaotic dynamical system to periodic motion by controlling the system about one of the many unstable periodic orbits embedded in the chaotic attractor, through only small time dependent perturbations in an accessible system parameter. They demonstrated their method numerically by controlling the Henon map. Far from being a numerical curiosity that requires experimentally unattainable precision, it was believed that this method can be widely implemented in a variety of systems including chemical, biological, optical, electronic, and mechanical systems. The method is based on the observation that unstable periodic orbits are dense in a typical chaotic attractor. Their method assumes only the following four points. First, the dynamics of the system can be represented as arising from an n-dimensional non-linear map. Second, there is a specific periodic orbit of the map which lies in the attractor and around which one wishes to stabilize the dynamics, and so on. To control the chaos, one attempts to confine the iterates of the map to a small neighborhood of the desired orbit.}, number={26}, journal={Physical Review Letters}, publisher={American Physical Society (APS)}, author={Ditto, W. L. and Rauseo, S. N. and Spano, M. L.}, year={1990}, month={Dec}, pages={3211–3214} }
 @article{ditto_spano_savage_rauseo_heagy_ott_1990, title={Experimental observation of a strange nonchaotic attractor}, volume={65}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0000374456&partnerID=MN8TOARS}, DOI={10.1103/PhysRevLett.65.533}, abstractNote={Evidence is presented for the existence of a strange nonchaotic attractor in a two-frequency quasiperiodically driven, buckled, magnetoelastic ribbon experiment. Scaling behavior in the Fourier amplitude spectrum is observed in agreement with predicted scaling behavior for strange nonchaotic attractors. Dimension measurements also support the existence of a strange nonchaotic attractor.}, number={5}, journal={Physical Review Letters}, author={Ditto, W.L. and Spano, M.L. and Savage, H.T. and Rauseo, S.N. and Heagy, J. and Ott, E.}, year={1990}, pages={533–536} }
 @article{ditto_rauseo_cawley_grebogi_hsu_kostelich_ott_savage_segnan_spano_et al._1989, title={Experimental observation of crisis-induced intermittency and its critical exponent}, volume={63}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-5844249871&partnerID=MN8TOARS}, DOI={10.1103/PhysRevLett.63.923}, abstractNote={Critical behavior associated with intermittent temporal bursting accompanying the sudden widening of a chaotic attractor was observed and investigated experimentally in a gravitationally buckled, parametrically driven, magnetoelastic ribbon. As the driving frequency, f, was decreased through the critical value, ${f}_{c}$, we observed that the mean time between bursts scaled as \ensuremath{\Vert}${f}_{c}$-f${\ensuremath{\Vert}}^{\mathrm{\ensuremath{-}}\ensuremath{\gamma}}$. .AE}, number={9}, journal={Physical Review Letters}, author={Ditto, W.L. and Rauseo, S. and Cawley, R. and Grebogi, C. and Hsu, G.-H. and Kostelich, E. and Ott, E. and Savage, H.T. and Segnan, R. and Spano, M.L. and et al.}, year={1989}, pages={923–926} }
 @article{ditto_pickett_1988, title={Nonperturbative solutions of nonlinear differential equations using continued fractions}, volume={29}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-36549096326&partnerID=MN8TOARS}, number={8}, journal={Journal of Mathematical Physics}, author={Ditto, W.L. and Pickett, T.J.}, year={1988}, pages={1761–1770} }